Details

Ognian Kassabov ^[a]

Characterizing a surface by invariants

Pages: 251-261
Received: 10 April 2019
Accepted in revised form: 19 November 2019
Mathematics Subject Classification (2010): 53A05.
Keywords: Surfaces, equations of Gauss and Codazzi, canonical principal parameters.
Author address:
[a]: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113, Sofia, Bulgaria

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. The principal curvatures or the Gauss and the mean curvature may be used as such a pair of invariants.

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