English

Characterizing a surface by invariants

Differential Geometry 2019-02-21 v2

Abstract

Canonical principal parameters are introduced for surfaces in R3\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.

Keywords

Cite

@article{arxiv.1902.02254,
  title  = {Characterizing a surface by invariants},
  author = {Ognian Kassabov},
  journal= {arXiv preprint arXiv:1902.02254},
  year   = {2019}
}

Comments

8 pages

R2 v1 2026-06-23T07:33:44.893Z