Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line
Abstract
It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R^3_1 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across the light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in R^{n+1}_1 that change type across an (n-1)-dimensional light-like plane.
Keywords
Cite
@article{arxiv.1211.4912,
title = {Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line},
author = {Shoichi Fujimori and Young Wook Kim and Sung-Eun Koh and Wayne Rossman and Heayong Shin and Masaaki Umehara and Kotaro Yamada and Seong-Deog Yang},
journal= {arXiv preprint arXiv:1211.4912},
year = {2013}
}
Comments
10 pages, 1 figure; Version 3: Sections 2 and 3 in Version 2 are removed, since they are not directly related to our main theorem in the revision