Hokkaido Mathematical Journal

Behavior of the Gaussian curvature of timelike minimal surfaces with singularities

Shintaro AKAMINE

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Hokkaido Math. J., Volume 48, Number 3 (2019), 537-568.

Dates
First available in Project Euclid: 14 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1573722017

Digital Object Identifier
doi:10.14492/hokmj/1573722017

Mathematical Reviews number (MathSciNet)
MR4031251

Zentralblatt MATH identifier
07145329

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 57R45: Singularities of differentiable mappings 53B30: Lorentz metrics, indefinite metrics

Keywords
Lorentz-Minkowski space timelike minimal surface Gaussian curvature wave front singularity

Citation

AKAMINE, Shintaro. Behavior of the Gaussian curvature of timelike minimal surfaces with singularities. Hokkaido Math. J. 48 (2019), no. 3, 537--568. doi:10.14492/hokmj/1573722017. https://projecteuclid.org/euclid.hokmj/1573722017


Export citation