Proceedings of the Japan Academy, Series A, Mathematical Sciences

An optimal inequality and an extremal class of graph hypersurfaces in affine geometry

Bang-Yen Chen

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We discover a general optimal inequality for graph hypersurfaces in affine $(n + 1)$-space $\mathbf{R}^{n+1}$ involving the Tchebychev vector field. We also completely classify the hypersurfaces which verify the equality case of the inequality.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 7 (2004), 123-128.

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

Primary: 53A15: Affine differential geometry
Secondary: 53C40: Global submanifolds [See also 53B25] 53B20: Local Riemannian geometry 53B25: Local submanifolds [See also 53C40]

Optimal inequality graph hypersurface extremal class


Chen, Bang-Yen. An optimal inequality and an extremal class of graph hypersurfaces in affine geometry. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 7, 123--128. doi:10.3792/pjaa.80.123.

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