Visual Contours and Planar Sections of Affine Immersions

Details Visual Contours and Planar Sections of Affine Immersions Visual Contours and Planar Sections of Affine Immersions

2010-03-30

arxiv.org/abs/1003.5795v2

Mathematics

Differential Geometry

The paper has been withdrawn by the author because it must be rewritten

Scientific paper

In this paper we consider planar sections and visual contours of co-dimension one affine immersions. The main theorem says that the third order Taylor expansion of the difference between the visual contour and planar section functions is exactly the cubic form. We also consider parameterizations on two dimensional affine immersions whose coordinate lines are geodesics, in one direction, and both planar sections and visual contours in the other direction. We call such coordinates parallel-meridian. Among other results, we show that any two dimensional affine sphere that admits parallel-meridian coordinates with a pole must be a quadric.

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