Differential Geometry
Zero mean curvature surfaces in L3 containing a light-like line
Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 975-978.

It is well known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space L3 have singularities (i.e. points where the induced metric degenerates) in general. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. In this Note, we give new examples of such surfaces.

Il est bien connu que les surfaces maximales de type espace et les surfaces minimales de type temps dans lʼespace L3 de Lorentz–Minkowski de dimension 3 possèdent en général des singularités. Ces deux types sont caracterisés comme des surfaces de courbure moyenne nulle. La Note considère le cas où le lieu des singularités consiste en une droite de type lumière, cette situation nʼayant semble-t-il pas encore été analysée. Dans cette Note, nous donnons de nouveaux exemples de telles surfaces.

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DOI: 10.1016/j.crma.2012.10.024
Fujimori, S. 1; Kim, Y.W. 2; Koh, S.-E. 3; Rossman, W. 4; Shin, H. 5; Takahashi, H. 6; Umehara, M. 7; Yamada, K. 8; Yang, S.-D. 2

1 Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan
2 Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea
3 Department of Mathematics, Konkuk University, Seoul 143-701, Republic of Korea
4 Department of Mathematics, Faculty of Science, Kobe University, Kobe 657-8501, Japan
5 Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea
6 Hakuho Girlsʼ High School, Yokohama 230-0074, Japan
7 Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
8 Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
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     title = {Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line},
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Fujimori, S.; Kim, Y.W.; Koh, S.-E.; Rossman, W.; Shin, H.; Takahashi, H.; Umehara, M.; Yamada, K.; Yang, S.-D. Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 975-978. doi : 10.1016/j.crma.2012.10.024. http://www.numdam.org/articles/10.1016/j.crma.2012.10.024/

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