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

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