Biconservative hypersurfaces with constant scalar curvature in space forms

2021/10/07 by Fu, Yu, Hong, Min-Chun, Yang, Dan +1 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.03438

Abstract

Biconservative hypersurfaces are hypersurfaces which have conservative stress-energy tensor with respect to the bienergy, containing all minimal and constant mean curvature hypersurfaces. The purpose of this paper is to study biconservative hypersurfaces Mⁿ with constant scalar curvature in a space form Nⁿ⁺¹(c). We prove that every biconservative hypersurface with constant scalar curvature in N⁴(c) has constant mean curvature. Moreover, we prove that any biconservative hypersurface with constant scalar curvature in N⁵(c) is ether an open part of a certain rotational hypersurface or a constant mean curvature hypersurface. These solve an open problem proposed recently by D. Fetcu and C. Oniciuc for n≤4.

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• Biconservative Weingarten surfaces with flat normal bundle in N⁴ (ε)

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