Characterizing spheres by an immersion in Euclidean spaces

Abstract

In this paper we study compact immersed orientable hypersurfaces in the Euclidean space Rn+1 and show that suitable restrictions on the tangential and normal components of the immersion give different characterizations of the spheres.

Keywords

• Hypersurface
• Conformal vector field
• Ricci curvature
• Position vector field