Perspectives on Biharmonic Maps and Submanifolds

Balmus, Adina

doi:10.1142/9789814261173_0025

Cited by 15 publications

(29 citation statements)

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“…Since in the case when κ 1 = 0 (i.e., c is a geodesic), the curve is trivially biharmonic, we immediately get: A similar result is known to hold in Riemannian geometry (see [2], [6], [14], [18]). …”

Section: Frenet Frame and Geodesic Curvaturesupporting

confidence: 53%

Biharmonic Curves in Finsler Spaces

Voicu¹

2014

Journal of the Korean Mathematical Society

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Abstract. Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, specific properties and existence of non-geodesic biharmonic curves for some classes of Finsler spaces. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

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Section: Frenet Frame and Geodesic Curvaturesupporting

confidence: 53%

Biharmonic Curves in Finsler Spaces

Voicu¹

2014

Journal of the Korean Mathematical Society

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“…However, Generalized Chen's conjecture is still open in its full generality for ambient spaces with constant sectional curvature. For more recent developments of Chen's conjecture and Generalized Chen's conjecture, for instance, see [1][2][3][10][11][12][13][14][15][16][17][18].…”

Section: Yu Fumentioning

confidence: 99%

On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb S^5$

2015

Proc. Amer. Math. Soc.

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“…Having in mind all these examples in spheres and in hyperbolic spaces, let us recall now another interesting property for surfaces and hypersurfaces, the biharmonicity. As the aim of our article does not consist in the study of biharmonicity, the reader is invited to check [1] for more details on the subject. In the end of this section we wold like to bring into attention some classical results concerning the biharmonicity of the surfaces and hypersurfaces above studied form the II-minimality point of view.…”

Section: Proofmentioning

confidence: 99%