Generalized Rotation Submanifolds in a Space Form

Abstract

Let \(\Phi : M^k \rightarrow R^p(c)\) be an isometric immersion of an k–dimensional Riemannian manifold into space form. We present, in a pure geometry way, the notion of the rotation immersion x generated by immersion Φ into \(R^m(c)(m > p)\), which is a generalization of classical rotation hypersurface. In addition, we investigate the differential geometry of rotation immersion generated by Φ in sphere space.