Affine normal curvature of hypersurfaces from the point of view of singularity theory期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Affine normal curvature of hypersurfaces from the point of view of singularity theory

Authors:	Declan Davis

Affiliation:	(1) Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool, L69 7ZL, UK

Abstract:	We consider smoothly embedded hypersurfaces ${M subset mathbb{R}^{n+1}}$ under the action of the special affine group ${{rm SL}(n+1,mathbb{R}) < imes mathbb{R}^{n+1}}$ . We construct a differential invariant, called affine normal curvature, which assigns to a point and a tangent direction a number. We prove some of its nice properties which connect it with affine principal directions, affine umbilics, and affine mean curvature.

Keywords:	Affine differential geometry Affine normal Singularity theory
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