Hypersurfaces with radial mean curvature in space forms

Abstract

In this paper, we study two classes of hypersurfaces, namely, the DRMChypersurfaces and the HDRMC-hypersurfaces in space forms M n+1(c), c = −1, 0, 1, these classes include the Weingarten hypersurfaces of the spherical type obtained in [10]. For n = 2, we present a way to obtain DRMC-surfaces and HDRMC-surfaces in M 3 (c) using two holomorphic functions. Also, we classify the DRMC-hypersurfaces of rotation in M n+1(c) and the HDRMC-hypersurfaces of rotation in R n+1 .