A topological lower bound for the energy of a unit vector field on a closed hypersurface of the euclidean space. The 3-dimensional case

Abstract

In this short note we prove that the degree of the Gauss map {\nu} of a closed 3-dimensional hypersurface of the Euclidean space is a lower bound for the total bending functional B, introduced by G. Wiegmink. Consequently, the energy functional E introduced by C. M. Wood admits a topological lower bound.