A Rigidity Result for Minimal Rotation Hypersurfaces of 5D Spaces of Constant Curvature

2023/04/17 by Aaron J. Tyrrell, Tyrrell, Aaron J.
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2304.08346

Abstract

In this paper we show that a particular extrinsic pointwise hypersurface invariant is always non-positive on minimal hypersurfaces of constant curvature spaces and vanishes identically if and only if the hypersurface is rotational. We show this for hypersurfaces of 5-dimensional spaces of constant curvature but we conjecture that this should generalize to a similar result in other dimensions.

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