A metric property of umbilic points

Details A metric property of umbilic points A metric property of umbilic points

2003-05-13

arxiv.org/abs/math/0305185v1

Mathematics

Differential Geometry

8 pages, 1 figure

Scientific paper

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this ratio with that reported by Berry and Hannay (1977) in the domain of Statistical Physics, is discussed.

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