Open Access
Research Article
Triharmonic Curves in Heisenberg Group
*Bendehiba SenoussiCorresponding authorsnoussi.bendehiba19@gmail.comDepartment of MathematicsEcole Normale Supérieure, Mostaganem, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 20 Feb 2021
- Accepted:
- 03 Feb 2022
- Published Online:
- 15 Jun 2022
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2022.2063407
- Pages:
- 55–65
Abstract
In this paper, we study triharmonic curves in Heisenberg group . We give necessary and sufficient conditions for helices to be triharmonic. We characterize the triharmonic curves in terms of their curvature and torsion.
Keywords
Subject Classifications
53C3053B25
References
- M.Barros. General helices and a theorem of Lancret . Proc. A.M.S ., 125 ( 1997 ), 1503 - 1509 . doi: 10.1090/S0002-9939-97-03692-7
- M.Barros, A.Ferrández, P.Lucas and M. A.Meroño, General helices in the 3-dimensional Lorentzian space forms , Rocky Mountain J. Math . 31 ( 2001 ), 373 - 388 . doi: 10.1216/rmjm/1020171565
- V.Branding, A structure theorem for polyharmonic maps between riemannian manifolds . arXiv preprint arXiv:1901.08445, 2019 .
- R.Caddeo, C.Oniciuc, P.Piu, Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group , Rend. Sem. Mat. Univ. Pol. Torino . Vol. 62 , 3 ( 2004 ), 265 - 278 .
- R.Caddeo, S.Montaldo, C.Oniciuc and P.Piu, The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces, Modern trends in geometry and topology , Cluj Univ. Press , Cluj-Napoca ( 2006 ), 121 - 131 .
- J.Eells and L.Lemaire, Selected topics in harmonic maps . CBMS. Am. Math. Soc . 50 ( 1983 ).
- D.Fetcu, Biharmonic curves in Cartan-Vranceanu (2n+1)-dimensional spaces , Contributions to Algebra and Geometry 46 ( 2 ) ( 2007 ), 513 - 521 .
- M.Goze - P.Piu, , Rend. Circ. Mat. Palermo , XXXIX-II ( 1990 ), 299 - 306 . doi: 10.1007/BF02844764
- S.Maeta. k-Harmonic Maps into a Riemannian Manifold with Constant Sectional Curvature . Proc. Amer. Math. Soc . 140 ( 2012 ), 1835 - 1847 . doi: 10.1090/S0002-9939-2011-11049-9
- S.Maeta. The Second variational formula of the k-Energy and k-Harmonic curves . Osaka J. Math . 49 ( 2012 ), 1035 - 1063 .
- S.Montaldo and A.Pampano, Triharmonic curves in 3-dimensional homogeneous spaces , arXiv:2008.10571v1. 2020 .
- D. J.Struik., Lectures on classical differential geometry . New York: Dover Publications, Inc ., 1988 . Zbl 0697.53002.
- S. B.Wang. The First Variation Formula for k-Harmonic Mapping . Journal of Nanchang University 13 ( 1989 ).
Views: 54Downloads: 73Citations: 1
