Surfaces with high contact number and their characterization

Revista De La Union Matematica Argentina, 2017

The object of the present paper is to characterize three-dimensional trans-Sasakian generalized Sasakian space forms admitting biharmonic almost contact curves with respect to generalized Tanaka Webster Okumura (gTWO) connections and to give illustrative examples. The mean curvature vector of almost contact curves has been analyzed on trans-Sasakian manifolds with gTWO connections. Some properties of slant curves on the same manifolds have been established. Finally curvature and torsion, with respect to gTWO connections, of C-parallel and C-proper slant curves in three-dimensional almost contact metric manifolds have been deduced.

Georgian Mathematical Journal

We study the conformal curvature tensor and the contact conformal curvature tensor in Sasakian and/or K-contact manifolds. We find a necessary and sufficient condition for a Sasakian manifold to be ϕ-conformally flat. We also find some necessary conditions for a K-contact manifold to be ϕ-contact conformally flat. Then we give a structure theorem for ϕ-contact conformally flat Sasakian manifolds. It is also proved that a Sasakian manifold cannot be ξ-contact conformally flat.

Journal of Geometry, 2008

Inspired by a result of Boyer and Galicki, we prove that a complete K-contact gradient soliton is compact Einstein and Sasakian. For the nongradient case we show that the soliton vector field is a Jacobi vector field along the geodesics of the Reeb vector field. Next we show that among all complete and simply connected K-contact manifolds only the unit sphere admits a non-Killing holomorphically planar conformal vector field (HP CV ). Finally we show that, if a (k, μ)-contact manifold admits a non-zero HP CV , then it is either Sasakian or locally isometric to E 3 or E n+1 × S n (4).

Differential Geometry from a Singularity Theory Viewpoint, 2015

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a normal paracontact metric manifold. Necessary and sufficient conditions are given for a subman-ifold to be a pseudo-slant submanifold, contact pseudo-slant product, mixed geodesic, D θ and D ⊥-geodesic in a normal paracontact metric manifold.

2006

We study the differential geometric properties of n-dimensional real submanifolds M of complex space forms M , whose maximal holomorphic tangent subspace is (n− 1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space. Using certain condition on the induced almost contact structure F and on the second fundamental form h of these submanifolds, which is sufficient for F to be the contact one, we give a classification of such submanifolds M and we obtain new characterizations of some model spaces in complex space forms.

Cubo, 2010

The object of the present paper is to study a type of contact metric manifolds, called N (k)contact metric manifolds admitting a non-null concircular and torse forming vector field. Among others it is shown that such a manifold is either locally isometric to the Riemannian product E n+1 (0) × S n (4) or a Sasakian manifold. Also it is shown that such a contact metric manifold can be expressed as a warped product I×ep * M , where ( * M , * g ) is a 2n-dimensional manifold. El objetivo del presente artículo es estudiar un tipo de variedades métricas de contacto, llamadas N (k)-variedades métricas de contacto admitiendo un campo de vectores concircular y forma torse. Es demostrado también que tales variedades son o localmente isométricas a productos Riemannianos E n+1 (0) × S n (4) o una variedade Sasakian. Es demostrado que tales variedades métricas de contacto pueden ser expresadas como un producto deformado I×ep * M , donde ( * M , * g ) es una variedad 2n-dimensional. 12, 1 (2010)

Symmetry

In this study, the authors focus on quasi-hemi-slant submanifolds (qhs-submanifolds) of (α,β)-type almost contact manifolds, also known as trans-Sasakian manifolds. Essentially, we give sufficient and necessary conditions for the integrability of distributions using the concept of quasi-hemi-slant submanifolds of trans-Sasakian manifolds. We also consider the geometry of foliations dictated by the distribution and the requirements for submanifolds of trans-Sasakian manifolds with quasi-hemi-slant factors to be totally geodesic. Lastly, we give an illustration of a submanifold with a quasi-hemi-slant factor and discuss its application to number theory.

Trends in Differential Geometry, Complex Analysis and Mathematical Physics - Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields, 2009

In this paper we study submanifolds of almost contact manifolds with Norden metric of codimension two with totally real normal spaces. Examples of such submanifolds as a Lie subgroups are constructed.

International Journal of Mathematics and Mathematical Sciences, 1983

Recently, K.Yano and M.Kon [5] have introduced the notion of a contactCR-submanifold of a Sasakian manifold which is closely similar to the one of aCR-submanifold of a Kaehlerian manifold defined by A. Bejancu [1].In this paper, we shall obtain some fundamental properties of contactCR-submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second fundamental form of a contactCR-product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contactCR-submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).