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Belarbi, Lakehal
- Some Biharmonic Problems on the Tangent Bundle with a Berger-type Deformed Sasaki Metric
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Authors
Affiliations
1 Department of Mathematics, University of Mascara, DZ
2 Department of Mathematics, University of Bechar, PO Box 417, 08000, Bechar, DZ
3 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (U.M.A.B.), B.P.227,27000, Mostaganem, DZ
1 Department of Mathematics, University of Mascara, DZ
2 Department of Mathematics, University of Bechar, PO Box 417, 08000, Bechar, DZ
3 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (U.M.A.B.), B.P.227,27000, Mostaganem, DZ
Source
The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 217–236Abstract
Let (M2k,Φ,g) be an almost anti-paraKahler manifold and TM its tangent bundle equipped with the Berger type deformed Sasaki metric gBS and the paracomplex structure Φ˜. In this paper, we deal with the biharmonicity of canonical projection π : TM →M and a vector field X which is considered as a map X : M → TM.Keywords
Berger type deformed Sasaki metric, anti-paraKahler manifold, harmonic maps, biharmonic map
References
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- Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces
Abstract Views :167 |
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Authors
Affiliations
1 Department of Mathematics, University of Mascara, DZ
2 Department of Mathematics,University of Bechar, DZ
3 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganemt, DZ
1 Department of Mathematics, University of Mascara, DZ
2 Department of Mathematics,University of Bechar, DZ
3 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganemt, DZ
Source
The Journal of the Indian Mathematical Society, Vol 89, No 3-4 (2022), Pagination: 263-277Abstract
In this paper, we study biharmonic curves in three-dimensio -nal generalized symmetric spaces, equipped with a left-invariant pseudo- Riemannian metric. We characterize non-geodesic biharmonic curves in three-dimensional generalized symmetric spaces and prove that there ex- ists no non-geodesic biharmonic spacelike helix in three-dimensional gen- eralized symmetric spaces. We also show that a linear map from a Eu- clidean space in three-dimensional generalized symmetric spaces is bihar- monic if and only if it is a harmonic map, and give a complete classification of such maps.
Keywords
Generalized Symmetric Spaces, Left-Invariant Metrics, Harmonic Curves, Biharmonic Curves, Pseudo-Riemannian Metrics.References
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- Ye-Lin Ou and Ze-Ping Wang, Biharmonic maps into sol and nil spaces., arXiv:math/0612329v1[math.DG]13 Dec 2006.
- V. Oproiu, On Harmonic Maps Between Tangent Bundles, Rend. Sem. Mat. 47(1989), 47-55.
- H. Mazouzi, H. El hendi and L. Belarbi, On the generalized bi-f-harmonic map equations on singly warped product manifolds, Comm. Appl. Nonlinear Anal. 25(3)(2018), 52 - 76.
- A. Medjadj, H. Elhendi and L. Belarbi, Some biharmonic problems on the tangent bundle with a Berger-type deformed Sasaki metric, J. Indian Math. Soc., 88(3-4)(2021),217-236.
- S. Yuksel Perktas and E Kilic, Biharmonic Curves in 3-Dimensional Hyperbolic Heisen-berg Group, arXiv:1103.0684 [math.DG] 4 Mar 2011.