Triharmonic CMC hypersurfaces in space forms with 4 distinct principal curvatures

2021/04/19 by Hang Chen, Chen, Hang, Zhida Guan +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C42 #msc:53C43 #msc:58E20

paper · pdf · doi:10.48550/arxiv.2104.09377

11 pages

arxiv created 2021/04/19 · arxiv updated 2021/04/20

Abstract

A triharmonic map is a critical point of the tri-energy in the space of smooth maps between two Riemannian manifolds. In this paper, we prove that if Mⁿ (n≥ 4) is a CMC proper triharmonic hypersurface in a space form ℝⁿ⁺¹(c) with four distinct principal curvatures and the multiplicity of the zero principal curvature is at most one, then M has constant scalar curvature. In particular, we obtain any CMC proper triharmonic hypersurface in ℝ⁵(c) is minimal when c≤ 0, which supports the generalized Chen's conjecture. We also give some characterizations of CMC proper triharmonic hypersurfaces in \mathbbS⁵.

Citations

• Harmonic Mappings of Riemannian Manifolds

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