Triharmonic hypersurfaces
WebJun 23, 2024 · A k-harmonic map is a critical point of the k-energy defined on the space of smooth maps between two Riemannian manifolds.In this paper, we prove that if \(M^{n} (n\ge 3)\) is a CMC proper triharmonic hypersurface with at most three distinct principal curvatures in a space form \(\mathbb {R}^{n+1}(c)\), then M has constant scalar curvature. Webtheory of triharmonic hypersurfaces in space forms and derive some useful lemmas, which are very important for us to study the geometric properties of triharmonic hypersurfaces. In Section 3, we give the proofs of Theorems 1.5 and 1.6. In Section 4, we finish the proofs of Theorems 1.8 and 1.9.
Triharmonic hypersurfaces
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WebApr 4, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site WebTriharmonic Riemannian submersions from 3-dimensional space forms. Tomoya Miura and Shun Maeta. 5 February 2024 Advances in Geometry, Vol. 21, No. 2. ... Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean 5-space. Yu Fu. 1 Jan 2014 Journal of Geometry and Physics, Vol. 75.
WebWe also give some characterizations of CMC proper triharmonic hypersurfaces in $\mathbb{S}^5$. A triharmonic map is a critical point of the tri-energy in the space of … WebAbstract. B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with constant mean curvature are minimal.
WebMar 5, 2024 · V ery recently, Chen-Guan investigated triharmonic CMC hypersurfaces in a space form N n +1 ( c ) under some assumptions on the number of distinct principal … WebJun 23, 2024 · A k-harmonic map is a critical point of the k-energy defined on the space of smooth maps between two Riemannian manifolds.In this paper, we prove that if \(M^{n} …
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WebDec 1, 2024 · Space forms. Closed hypersurfaces. 1. Introduction. The theory of biharmonic maps plays a fundamental role in many branches of Partial Differential Equations and Differential Geometry. The notion of biharmonic maps, as a natural generalization of harmonic maps, was introduced in 1964 by Eells and Sampson [6], and the related … entegra coach ethos 20aWebtriharmonic cmc hypersurfaces in r-5(c) manuscripta mathematica: a: t3: 3 区: 西北工业大学: 陈亚萍: a physical-constraint-preserving finite volume weno method for special … dr. gloria graham newton mshttp://export.arxiv.org/abs/2303.02612 dr gloria fleming westerville ohWebA triharmonic hypersurfaces in Nn+1(c) is called proper if it is not minimal. In the following, we will consider a CMC proper hypersurface Mn in a space form Nn+1(c). Then (2.6) … dr gloria chu athens gaWebIn geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.A hypersurface is a manifold or an algebraic variety of dimension n − 1, which … entegra conorstone walkthruWebAs an application, we give the complete classification of the 3-dimensional closed proper CMC triharmonic hypersurfaces in $\mathbb{S}^{4}$. ... entegra coach tech supportWeb214 V. Branding Arch. Math. where ∇¯ represents the connection on φ∗TN.The solutions of τ(φ)=0are calledharmonic maps ... entegra odyssey 31f 2022 standard features