A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture

Details A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture

2005-03-14

arxiv.org/abs/math/0503249v1

Mathematics

Differential Geometry

This paper was accepted for publication in International Journal of Mathematics

Scientific paper

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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