Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
References
All Topics
Mathematics
Pure Mathematics

Conformal anti-invariant $\xi^\perp-$submersions

Profile image of yılmaz Gunduzalpyılmaz Gunduzalp

2017, arXiv (Cornell University)

Abstract

As a generalization of anti-invariant ξ ⊥ −Riemannian submersions, we introduce conformal anti-invariant ξ ⊥ −submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find necessary and sufficient conditions for a conformal anti-invariant ξ ⊥ −submersion to be totally geodesic and harmonic, respectively. Moreover, we show that there are certain product structures on the total space of a conformal anti-invariant ξ ⊥ −submersion.

Related papers

Conformal Hemi-Slant Submersions from Almost Hermitian Manifolds
Shashikant Pandey

Communications of The Korean Mathematical Society, 2020

In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from Kähler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.

View PDFchevron_right
Geometrical Aspect of Pointwise Semi-Slant Conformal Submersions
Mohd Bilal

International journal of analysis and applications, 2024

The aim of this paper is to define pointwise semi-slant conformal submersions from locally product Riemannian manifolds onto Riemannian manifolds. We investigated the conditions under which the distributions are integrable and the leaves of the distributions defines totally geodesic foliation. Additionally, we examined the concept of pluriharmonicity of pointwise semi-slant conformal submersions. In support of the results we obtained, we present non-trivial examples.

View PDFchevron_right
Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds
Irem KUPELI ERKEN

TURKISH JOURNAL OF MATHEMATICS, 2016

The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic vector field ξ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field ξ is a horizontal vector field and an anti-invariant horizontally conformal submersion such that ξ is a vertical vector field.

View PDFchevron_right
Semi-Slant Pseudo-Riemannian Submersions from Indefinite Almost Contact 3-STRUCTURE Manifolds Onto Pseudo-Riemannian Manifolds
Uma Shankar Verma

2017

In this paper, we introduce the notion of a semi-slant pseudoRiemannian submersion from an indefinite almost contact 3-structure manifold onto a pseudo-Riemannian manifold. We investigate the geometry of foliations determined by horizontal and vertical distributions and provide a non-trivial example. We also find a necessary and sufficient condition for a semi-slant submersion to be totally geodesic. Moreover, we check the harmonicity of such submersions.

View PDFchevron_right
Almost contact submersions with total space a locally conformal cosymplectic manifold
juan rocha

Annales de la faculté des sciences de Toulouse Mathématiques, 1995

Almost contact submersions with total space a locally conformal cosymplectic manifold Annales de la faculté des sciences de Toulouse 6 e série, tome 4, n o 3 (1995), p. 473-517 <http://www.numdam.org/item?id=AFST_1995_6_4_3_473_0> © Université Paul Sabatier, 1995, tous droits réservés. L'accès aux archives de la revue « Annales de la faculté des sciences de Toulouse » (http://picard.ups-tlse.fr/~annales/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Almost contact submersions with total space a locally conformal cosymplectic manifold(*)

View PDFchevron_right
Hemi-slant submersions from almost product Riemannian manifolds
yılmaz Gunduzalp

Gulf Journal of Mathematics

In this paper, we introduce hemi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a hemi-slant submersion to be totally geodesic.

View PDFchevron_right
Riemannian submersions from almost contact metric manifolds
Raluca Mocanu

2011

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.

View PDFchevron_right
Generalized horizontally weakly conformal submersion between semi-Riemannian manifold
mohammed jamali

Afrika Matematika, 2015

In this article we obtain the condition for the existence of generalized horizontally weakly conformal (HWC) submersion between degenerate manifolds. Moreover we conclude some results based on the curvature of HWC submersion.

View PDFchevron_right
Clairaut conformal submersions
Akhilesh Yadav

2022

The aim of this paper is to introduce Clairaut conformal submersion between Riemannian manifolds. First, we find necessary and sufficient conditions for a regular curve to be geodesic on the total and base manifold of conformal submersion. Further, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. Moreover, we find a necessary and sufficient condition for a Clairaut conformal submersion to be harmonic. Finally, we give a non-trivial example of Clairaut conformal submersion using doubly warped product.

View PDFchevron_right
Conformal and Isometric Immersions of Riemannian Manifolds
Isabel Salavessa

Mathematische Zeitschrift, 1987

View PDFchevron_right

References (45)

  1. Akyol, M. A., Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics, (In Press), Doi: 10.15672/HJMS.20174720336, (2016).
  2. Akyol, M. A., Sarı, R. and Aksoy, E., Semi-invariant ξ ⊥ -Riemannian submersions from almost contact metric manifolds, Int. J. Geom. Methods Mod. Phys., (Accepted), (2017).
  3. Akyol, M. A. and S ¸ahin B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish J. Math. 40, (2016), 43-70.
  4. Akyol, M. A. and S ¸ahin B., Conformal semi-invariant submersions, Communications in Con- temporary Mathematics, (In press), DOI: 10.1142/S02191997165001151650011.
  5. Blair, D. E., Contact manifold in Riemannain geometry, Lecture Notes in Math. 509, Springer- Verlag, Berlin-New York, (1976).
  6. Baird, P. and Wood, J. C., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press. Ox- ford, 2003.
  7. Beri, A., Erken, İ. K. and Murathan, C., Anti-invariant Riemannian submersions from Ken- motsu manifolds onto Riemannian manifolds, 40(3), (2016), 540-552.
  8. Cengizhan, M. and Erken, I. K., Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian submersions, Filomat. 29(7), (2015), 1429-1444.
  9. Chen, B. Y., Riemannian submanifolds, Handbook of differential geometry. North-Holland, Amsterdam Vol. I, 2000, 187-418.
  10. Chinea, D., Harmonicity on maps between almost contact metric manifolds. Acta Math. Hun- gar. (2010); 126(4): 352-365.
  11. Chinea, D., Harmonicity of holomorphic maps between almost Hermitian manifolds. Canad. Math. Bull. (2009); 52(1): 18-27.
  12. Chinea, D., On horizontally conformal (φ, φ ′ )-holomorphic submersions. Houston J. Math. (2008); 34(3): 721-737.
  13. Chinea, D., Almost contact metric submersions. Rend. Circ. Mat. Palermo, (1985), 34(1): 89-104.
  14. Fuglede, B., Harmonic Morphisms Between Riemannian Manifolds, Ann. Inst. Fourier (Greno- ble) 28 (1978), 107-144.
  15. Falcitelli, M., Ianus, S. and Pastore, A. M., Riemannian submersions and Related Topics. World Scientific, River Edge, NJ, 2004.
  16. Gilkey, P., Itoh, M. and Park, J., Anti-invariant Riemannian submersions: A Lie-theoretical Approach, Taiwanese J. Math, 20(4), (2016), 787-800.
  17. Gundmundsson, S., The Geometry of Harmonic Morphisms, Ph.D. Thesis, University of Leeds, (1992).
  18. Gundmundsson, S. and Wood, J. C., Harmonic Morphisms between almost Hermitian mani- folds, Boll. Un. Mat. Ital. B. (1997), 11(2):185-197.
  19. Gündüzalp, Y., Slant submersions from almost product Riemannian manifolds, Turkish J. Math., 37: 863-873 (2013).
  20. Gündüzalp, Y., Anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds, Journal of Function Spaces and Applications, Volume 2013, Article ID 720623, 7 pages.
  21. Gündüzalp, Y., Anti-invariant Riemannian submersions from almost product Riemannian manifolds, Mathematical Science and Applications E-notes. 1(1), (2013), 58-66.
  22. Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  23. Ishıhara, T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. kyoto Univ. 19 (1979), 215-229.
  24. Lee, J. W., Anti-invariant ξ ⊥ -Riemannian submersions from almost contact manifolds, Hacettepe Journal of Mathematics and Statistic, 42(3), (2013), 231-241.
  25. Lee, J. C., Park, J. H., S ¸ahin B. and Song D. Y., Einstein conditions for the base space of anti- invariant Riemannian submersions and Clairaut submersions, Taiwanese J. Math. In press. DOI: 10.11650/tjm.19.2015.5283.
  26. Ianus, S., Ionescu, M., Mazzocco, R. and Vilcu, G. E., Riemannian submersions from almost contact metric manifolds, Abh. Math. Semin. Univ. Hamb. 81(2011), no:1, 101-114.
  27. Ianus, S., Mazzocco, R. and Vilcu, G. E., Riemannian submersions from quaternionic mani- folds, Acta Appl. Math., (2008), 104(1), 83-89.
  28. O'Neill, B., The fundamental equations of a submersion. Mich. Math. J., 1966, 13, 458-469.
  29. Ornea, L. and Romani, G., The fundamental equations of a conformal submersions, Beitrague Z. Algebra and Geometrie Contributions Algebra and Geometry, 34 (2), (1993), 233-243.
  30. Park, K. S. and Prasad, R., H-anti-invariant submersions from almost quaternionic Hermitian manifolds, arXiv:1507.04473 [math.DG].
  31. Park, K. S. and Prasad, R., Semi-slant submersions. Bull. Korean Math. Soc. 50 (2013), no. 3, 951-962.
  32. Park, K. S., h-semi-invariant submersions. Taiwanese J. Math. 16 (2012), no. 5, 18651878.
  33. Park, K. S., h-slant submersions. Bull. Korean Math. Soc. 49 (2012), no. 2, 329338.
  34. Ponge, R. and Reckziegel, H., Twisted products in pseudo-Riemannian geometry,Geom. Ded- icata. 1993; 48(1):15-25.
  35. Shahid, A. and Tanveer, F., Anti-invariant Riemannian submersions from nearly Kählerian mani-folds, Filomat 27(7)(2013) 1219-1235.
  36. Shahid, A. and Tanveer, F., Generic Riemannian submersions, Tamkang Journal of Mathe- matics, Volume 4, Number 4, (2013), 395-409. doi:10.5556/j.tkjm.44.2013.1211.
  37. Sasaki, S. and Hatakeyama, Y., On differentiable manifolds with contact metric structure, J. Math. Soc. Japan, 14, 249-271, 1961.
  38. S ¸ahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. European J. Math, no. 3, (2010), 437-447.
  39. S ¸ahin, B., Semi-invariant Riemannian submersions from almost Hermitian manifolds, Canad. Math. Bull, 56 (2011), 173.
  40. S ¸ahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 1 (2011), 93-105.
  41. S ¸ahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math., 17, No. 2, (2012), 629-659.
  42. Taştan, H. M., On Lagrangian submersions, Hacettepe J. Math. Stat. 43(6), (2014) 993-1000.
  43. Watson, B., Almost Hermitian submersions, J. Differential Geometry, 11(1), 1976, 147-165.
  44. Urakawa, H., Calculus of Variations and Harmonic Maps, Amerikan Math. Soc. 132, (1993).
  45. Yano, K. and Kon, M., Structures on Manifolds, World Scientific, Singapore, 1984. Bingöl University, Faculty of Arts and Sciences, Deparment of Mathematics, 12000, Bingöl, Turkey E-mail address: mehmetakifakyol@bingol.edu.tr

Related papers

Conformal semi-invariant ξ ^⊥-submersions from almost contact metric manifolds
Shashikant Pandey, Dr. Punam Gupta

2020

The purpose of the present paper is to introduce the conformal semi-invariant ξ ^⊥-Riemannian submersions from almost contact metric manifolds onto Riemannian manifolds as a generalization of anti-invariant submersions, semi-invariant submersions, anti-invariant ξ ^⊥-submersions, semi-invariant ξ ^⊥ ^⊥-submersions, conformal semi-invariant submersions. We obtain characterizations and investigate the integrability of distributions which are arisen from the definition of conformal semi-invariantξ^⊥-Riemannian submersions. We find out the necessary and sufficient conditions for a conformal semi-invariantξ^⊥-Riemannian submersions to be totally geodesic and harmonic. Finally, examples are also given for conformal semi-invariant submersions with horizontal Reeb vector field.

View PDFchevron_right
Conformal slant submersions from cosymplectic manifolds
yılmaz Gunduzalp

TURKISH JOURNAL OF MATHEMATICS, 2018

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field ξ is a vertical vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions and conformal anti-invariant submersions. More precisely, we mention lots of examples and obtain the geometries of the leaves of ker π * and (ker π *) ⊥ , including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we consider a decomposition theorem on total space of the new submersion.

View PDFchevron_right
Anti-Invariant Riemannian Submersions from Almost Product Riemannian Manifolds
yılmaz Gunduzalp

2013

In this paper, we introduce anti-invariant Riemannian submersions from almost product Riemannian manifolds onto Riemannian manifolds.We give an example, investigate the geometry of foliations which are arisenfrom the definition of a Riemannian submersion and check the harmonicity ofsuch submersions

View PDFchevron_right
Remarks on conformal anti-invariant Riemannian maps to cosymplectic manifolds
yılmaz Gunduzalp

Hacettepe Journal of Mathematics and Statistics, 2021

M.A. Akyol and B. Şahin [Conformal anti-invariant Riemannian maps to Kaehler manifolds, U.P.B. Sci. Bull., Series A, Vol. 80, Iss. 4, 2018] defined and studied the notion of conformal anti-invariant Riemannian maps to Kaehler manifolds. In this paper, as a generalization of totally real submanifolds and anti-invariant Riemannian maps, we extend this notion to almost contact metric manifolds. In this manner, we introduce conformal anti-invariant Riemannian maps from Riemannian manifolds to cosymplectic manifolds. In order to guarantee the existence of this notion, we give a non-trivial example, investigate the geometry of foliations which are arisen from the definition of a conformal Riemannian map and obtain decomposition theorems by using the existence of conformal Riemannian maps. Moreover, we investigate the harmonicity of such maps and find necessary and sufficient conditions for conformal anti-invariant Riemannian maps to be totally geodesic. Finally, we study weakly umbilical ...

View PDFchevron_right
Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds
Mobin Ahmad

2020

In this paper, we study an anti-invariant semi-Riemmannian submersions from indefinite almost contact metric manifolds. We obtain, the necessary and sufficient conditions for the characteristics vector filed to be vertical and horizontal. aMoreover, we find the conditions of integrability and hormonicness of this submersion map. Finally, we furnish an example of an anti-invariant semi-Riemannian submersion from indefinite almost contact metric manifold which is indefinite trans-Sasakian manifolds in the present paper.

View PDFchevron_right

Related topics

  • Mathematics
  • Pure Mathematics
  • Pure Mathematics(Differential Ge...
    • 580 California St., Suite 400
    San Francisco, CA, 94104
    © 2025 Academia. All rights reserved