Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 48, Number 3 (2019), 537-568.
Behavior of the Gaussian curvature of timelike minimal surfaces with singularities
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.
Hokkaido Math. J., Volume 48, Number 3 (2019), 537-568.
First available in Project Euclid: 14 November 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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