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An Optimal Inequality and Extremal Classes of Affine Spheres in Centroaffine Geometry

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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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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824-1027, U.S.A

    Bang-Yen Chen

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  1. Bang-Yen Chen
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Correspondence to Bang-Yen Chen.

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Chen, BY. An Optimal Inequality and Extremal Classes of Affine Spheres in Centroaffine Geometry. Geom Dedicata 111, 187–210 (2005). https://doi.org/10.1007/s10711-004-4199-4

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  • DOI: https://doi.org/10.1007/s10711-004-4199-4

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