A Note on Shape Vector Fields on Hypersurfaces

Abstract

In this paper, we initiate the study of shape vector fields on the hypersurfaces of a Riemannian manifold. We use a shape vector field on a compact hypersurface of a Euclidean space to obtain a characterization of round spheres. We also find a condition, under which a shape vector field that is on a compact hypersurface of a Euclidean space is a Killing vector field.

Keywords

• shape vector fields
• conformal vector fields
• Killing vector fields
• Euclidean space
• Ricci curvature
• spheres