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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Abstract

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

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

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442328

Digital Object Identifier
doi:10.3792/pjaa.80.123

Mathematical Reviews number (MathSciNet)
MR2094532

Zentralblatt MATH identifier
1076.53010

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

Keywords
Optimal inequality graph hypersurface extremal class

Citation

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. https://projecteuclid.org/euclid.pja/1116442328


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References

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