Abstract
A hypersurface f : M → Rn+1 in an affine (n+1)-space is called centroaffine if its position vector is always transversal to f*(TM) in Rn+1. In this paper, we establish a general optimal inequality for definite centroaffine hypersurfaces in Rn+1 involving the Tchebychev vector field. We also completely classify the hypersurfaces which verify the equality case of the inequality.
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