Abstract
Let n, ν be integers such that n≥2 and 0≤ν≤n+1. Let Mc,νn+1 be a (n+1)-dimensional semi-Riemannian space form of constant sectional curvature c and index ν. We give the parametrizations of rotation hypersurfaces in Mc,νn+1. Adding the condition for the r-th mean curvature to be constant, we show the study of these hypersurfaces is reduced to the study of a function on two variables. As an illustrative example, we study the particular case of rotation hypersurfaces with constant scalar curvature in Mc,νn+1, determining the values of n,c,ν for which these hypersurfaces are isoparametric. In the final part we study the variation of the second fundamental form of rotation hypersurfaces in order to obtain some rigidity results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.