Abstract

We deal with complete hypersurfaces with two distinct principal curvatures in a locally symmetric Riemannian manifold, which is supposed to obey some appropriated curvature constraints. Initially, considering the case that such a hypersurface has constant mean curvature, we apply a Simons type formula jointly with the well known generalized maximum principle of Omori–Yau to show that it must be isometric to an isoparametric hypersurface of the ambient space. Afterwards, we use a Cheng–Yau modified operator in order to obtain a sort of extension of this previously mentioned result for the context of linear Weingarten hypersurfaces, that is, hypersurfaces whose mean and scalar curvatures are linearly related.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.