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An Optimal Inequality and Extremal Classes of Affine Spheres in Centroaffine Geometry |
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| Authors: | |
| Institution: | (1) Department of Mathematics, Michigan State University, East Lansing, MI, 48824-1027, U.S.A |
| 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. |
| Keywords: | optimal inequality affine sphere centroaffine geometry extremal classes |
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