arXiv 1808.096412018-08math.DG

Analysis of timelike Thomsen surfaces - with deformations and singularities

Shintaro Akamine, Joseph Cho, Yuta Ogata

发表信息：: J. Geom. Anal. 30(1):731-761, 2020
DOI：: 10.1007/s12220-019-00166-7

英文摘要：

Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike minimal surfaces, to obtain a complete global classification of these surfaces and to characterize them using a geometric invariant called lightlike curvatures. As a result, we reveal the relationship between timelike Thomsen surfaces, and timelike minimal surfaces with planar curvature lines. As an application, we give a deformation of null curves preserving the pseudo-arclength parametrization and the constancy of the lightlike curvatures.

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