Springer Proceedings in Mathematics & Statisticsbook series (PROMS, volume 211)
巻, 号, ページ
Vol. 211
pp. 253--273
出版年月
2018年3月4日
出版者
和文:
英文:
Springer International Publishing
会議名称
和文:
英文:
International Meeting on Lorentzian Geometry GELOMA 2016
開催地
和文:
英文:
アブストラクト
With several concrete examples of zero mean curvature surfaces in the Lorentz-Minkowski 3-space R^3_1 containing a light-like line recently having been found, here we construct all real analytic germs of zero mean curvature surfaces by applying the Cauchy-Kovalevski theorem for partial differential equations. A point where the first fundamental form of a surface degenerates is said to be light-like. We also show a theorem on a property of light-like points of a surface in R^3_1 whose mean curvature vector is smoothly extendable. This explains why such surfaces will contain a light-like line when they do not change causal types. Moreover, several applications of these two results are given.
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