Chern conjecture on minimal hypersurfaces
Differential Geometry
2021-04-30 v1
Abstract
In this paper, we study -dimensional complete minimal hypersurfaces in a unit sphere. We prove that an -dimensional complete minimal hypersurface with constant scalar curvature in a unit sphere with constant is isometric to the totally geodesic sphere or the Clifford torus if , where denotes the squared norm of the second fundamental form of this hypersurface.
Cite
@article{arxiv.2104.14057,
title = {Chern conjecture on minimal hypersurfaces},
author = {Qing-Ming Cheng and Guoxin Wei and Takuya Yamashiro},
journal= {arXiv preprint arXiv:2104.14057},
year = {2021}
}