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A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture

Yuncherl Choi·Hyuk Kim
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Abstract

Eastwood and Ezhov generalized the Cayley surface to the Cayley hypersurface in each dimension, proved some characteristic properties of the Cayley hypersurface and conjectured that a homogeneous hypersurface in affine space satisfying these properties must be the Cayley hypersurface. We will prove this conjecture when the domain bounded by a graph of a function defined on $\R^n$ is also homogeneous giving a characterization of Cayley hypersurface. The idea of the proof is to look at the problem of affine homogeneous hypersurfaces as that of left symmetric algebras with a Hessian type inner product. This method gives a new insight and powerful algebraic tools for the study of homogeneous affine hypersurfaces.

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Yuncherl Choi, Hyuk Kim. 2005-03-14. A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture. https://arxiv.org/abs/math/0503249

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