Totally quasi-umbilic timelike surfaces in ℝ^1,2

2010/06/22 by Jeanne N. Clelland, Clelland, Jeanne N.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1006.4380

19 pages

openalex publication_date 2010/06/22 · arxiv created 2010/11/05 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a regular surface in Euclidean space ℝ³, umbilic points are precisely the points where the Gauss and mean curvatures K and H satisfy H²=K; moreover, it is well-known that the only totally umbilic surfaces in ℝ³ are planes and spheres. But for timelike surfaces in Minkowski space ℝ^1,2, it is possible to have H²=K at a non-umbilic point; we call such points \em quasi-umbilic, and we give a complete classification of totally quasi-umbilic timelike surfaces in ℝ^1,2.

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