On Hypersurfaces with two Distinct Principal Curvatures in Space Forms

Proceedings Mathematical Sciences

Bing Ye Wu¹ 

[1] Department of Mathematics, Minjiang University, Fuzhou, Fujiang 00, China$$

关键词: Hypersurface;    space forms;    principal curvature;    mean curvature.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We investigate the immersed hypersurfaces in space forms $mathbb{N}^{n+1}(c),n≥ 4$ with two distinct non-simple principal curvatures without the assumption that the (high order) mean curvature is constant. We prove that any immersed hypersurface in space forms with two distinct non-simple principal curvatures is locally conformal to the Riemannian product of two constant curved manifolds. We also obtain some characterizations for the Clifford hypersurfaces in terms of the trace free part of the second fundamental form.

【 授权许可】

Unknown