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arXiv · 1902.02254

Characterizing a surface by invariants

Ognian Kassabov
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Abstract

Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial differential equation equivalent to the Gauss equation. As such a pair of invariants we may use the principal curvatures or the Gauss and the mean curvature.

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Ognian Kassabov. 2019-02-06. Characterizing a surface by invariants. https://arxiv.org/abs/1902.02254

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