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October 2019 Behavior of the Gaussian curvature of timelike minimal surfaces with singularities
Shintaro AKAMINE
Hokkaido Math. J. 48(3): 537-568 (October 2019). DOI: 10.14492/hokmj/1573722017

Abstract

We prove that the sign of the Gaussian curvature, which is closely related to the diagonalizability of the shape operator, of any timelike minimal surface in the 3-dimensional Lorentz-Minkowski space is determined by the degeneracy and the signs of the two null regular curves that generate the surface. We also investigate the behavior of the Gaussian curvature near singular points of a timelike minimal surface with some kinds of singular points, which is called a minface. In particular we determine the sign of the Gaussian curvature near any non-degenerate singular point of a minface.

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Shintaro AKAMINE. "Behavior of the Gaussian curvature of timelike minimal surfaces with singularities." Hokkaido Math. J. 48 (3) 537 - 568, October 2019. https://doi.org/10.14492/hokmj/1573722017

Information

Published: October 2019
First available in Project Euclid: 14 November 2019

MathSciNet: MR4031251
zbMATH: 07145329
Digital Object Identifier: 10.14492/hokmj/1573722017

Subjects:
Primary: 53A10
Secondary: 53B30, 57R45

Rights: Copyright © 2019 Hokkaido University, Department of Mathematics

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Vol.48 • No. 3 • October 2019
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