A characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture

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dc.creatorChoi, Yuncherl
dc.creatorKim, Hyuk
dc.date2005-03-14
dc.date.accessioned2026-07-07T05:17:55Z
dc.date.available2026-07-07T05:17:55Z
dc.descriptionEastwood 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.
dc.descriptionThis paper was accepted for publication in International Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0503249
dc.identifierhttp://arxiv.org/abs/math/0503249
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74478
dc.subjectDifferential Geometry
dc.subjectRings and Algebras
dc.subject53A15, 17D25, 53B05
dc.titleA characterization of Cayley Hypersurface and Eastwood and Ezhov conjecture
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