Papers by Belarbi Lakehal
In this paper, we investigate the harmonicity and biharmonicity of a tangent map φ : (T M, g s ) ... more In this paper, we investigate the harmonicity and biharmonicity of a tangent map φ : (T M, g s ) → (T N, h s ) in the case where the tangent bundles T M, T N are endowed with Sasaki Riemannian metrics g s , h s .
On paraquaternionic submersions of tangent bundle of order two
Nonlinear Studies, 2018
In this paper we will show mainly that the canonical projection of the tangent bundle of order tw... more In this paper we will show mainly that the canonical projection of the tangent bundle of order two,endowed with the diagonal metric,of an almost paraquaternionic Hermitian manifolds is a paraquaternionic submersion and we obtain necessarily and sufficient conditions for the total space of this projection to be paraquaternionic K\"{a}hler or locally hyper para-K\"{a}hler manifold.
In this paper,we give some results in Riemannian manifold M with density eφ and we give examples ... more In this paper,we give some results in Riemannian manifold M with density eφ and we give examples of minimal surfaces in Euclidean 3-space with density.
SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 2020
In this paper, we show that the Legendre curves on three-dimensional Lorentzian Heisenberg space ... more In this paper, we show that the Legendre curves on three-dimensional Lorentzian Heisenberg space (H 3 , g) are locally φ-symmetric if and only if they are geodesic. Moreover, we prove that the Legendre curves on threedimensional Lorentzian Heisenberg space are biharmonic if and only if they are pseudo-helix.
SERIES III - MATEMATICS, INFORMATICS, PHYSICS, 2020
Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a n... more Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle T M . We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (T M, G f ) .
Annales Mathematicae et Informaticae, 2019
In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dim... more In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dimensional Heisenberg group which are invariant under the 1-parameter groups of isometries.
Lecture Notes in Computer Science, 2013
In this paper,we study the Plateau's problem in IR 3 with density and we give prove that divϕN = ... more In this paper,we study the Plateau's problem in IR 3 with density and we give prove that divϕN = −2Hϕ in a Riemannian manifold IM 3 with density Ψ = e ϕ ,where Hϕ and N are the ϕ−mean curvature and the unit normal vector field of a surface S in IM 3 with density.
Minimal translation surfaces in Lorentz Heisenberg space (ℋ3, g2)
Journal of Interdisciplinary Mathematics, 2021
Abstract The aim of this work is the classification of some types of minimal translation surfaces... more Abstract The aim of this work is the classification of some types of minimal translation surfaces in the 3–dimensional Lorentzian Heisenberg space ℋ3 endowed with the left invariant metric
On the ruled minimal surfaces in Heisenberg 3-space with density
Journal of Interdisciplinary Mathematics, 2020
Abstract In this paper, we give a description of ruled minimal surfaces by geodesics straight lin... more Abstract In this paper, we give a description of ruled minimal surfaces by geodesics straight lines in Heisenberg space ℍ3 with linear density (in particular ϕ(x, y, z) = α x and ϕ(x, y, z) = β y). Also we characterize the ∞ – Bakry-Émery Ricci curvature tensor and the ϕ - scalar curvature of Heisenberg space H3 with radial density e-aρ +c where
In this paper, we investigate the harmonicity of a tangent map ϕ : (T M,g) −→ (T N,h), in the cas... more In this paper, we investigate the harmonicity of a tangent map ϕ : (T M,g) −→ (T N,h), in the case when the tangent bundles T M and T N are endowed with natural Riemannian metricsg,h. In this work we generalize previous results related to the article of A. Sanini [24]. M.S.C. 2010: 53A45; 53C20.
In this paper, we give a description of ruled minimal surfaces by geodesics straight lines in Hei... more In this paper, we give a description of ruled minimal surfaces by geodesics straight lines in Heisenberg space H 3 with linear density = = , = .
In this paper, we show that the Legendre curves on three-dimensional Lorentzian Heisenberg space ... more In this paper, we show that the Legendre curves on three-dimensional Lorentzian Heisenberg space (H 3 , g) are locally φ-symmetric if and only if they are geodesic. Moreover, we prove that the Legendre curves on three-dimensional Lorentzian Heisenberg space are biharmonic if and only if they are pseudo-helix. 2000 Mathematics Subject Classification: 53C50, 53B30.
In this work we consider the three-dimensional Lie group denoted by H 2 × R, equipped with left-i... more In this work we consider the three-dimensional Lie group denoted by H 2 × R, equipped with left-invariant Riemannian metric. The existence of non-trivial (i.e., not Einstein) Ricci solitons on three-dimensional Lie group H 2 × R is proved. Moreover, we show that there are not gradient Ricci solitons.
We consider the five-dimensional solvable Lie group, equipped with left-invariant Riemannian metr... more We consider the five-dimensional solvable Lie group, equipped with left-invariant Riemannian metric. We obtain a full classification of Killing and affine vector fields as well as Ricci, curvature and matter collineations. Mathematics Subject Classification: 53C50, 53B30.
In this work we consider the Sol 3 Lie group, equipped with the left-invariant metric, Lorentzian... more In this work we consider the Sol 3 Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.
Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a n... more Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle T M. We calculate its Levi-Civita connection and Rieman-nian curvature tensor. We study the geometry of (T M, G f). 2000 Mathematics Subject Classification: 58A03, 58A05.
In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dim... more In this work we study constant extrinsically Gaussian curvature translation surfaces in the 3-dimensional Heisenberg group which are invariant under the 1-parameter groups of isometries.
Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a ne... more Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f,h and called twisted Sasaki matric on the tangent bundle T M. We studied the geometry of (T M, G f,h) by giving a relationships of the curvatures, Einstein structure, scalar and sectional curvatures between (T M, G f,h) and (M, g). MSC : 58A03, 58A05.
In this paper, we investigate the harmonicity and biharmonicity of a tangent map φ : (T M, g s) →... more In this paper, we investigate the harmonicity and biharmonicity of a tangent map φ : (T M, g s) → (T N, h s) in the case where the tangent bundles T M, T N are endowed with Sasaki Riemannian metrics g s , h s .
We consider the five-dimensional solvable Lie group, equipped with any left-invariant metric, eit... more We consider the five-dimensional solvable Lie group, equipped with any left-invariant metric, either Lorentzian or Riemannian. The existence of non-trivial (i.e., not Einstein) Ricci solitons on both Lorentzian and Rie-mannian five-dimensional solvable Lie group is proved. Moreover, we show that there are no gradient Ricci solitons.
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Papers by Belarbi Lakehal