On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups

IF 0.8 3区 数学 Q2 MATHEMATICS
Giovanni Calvaruso, Marco Castrillón-Lopez, Lorenzo Pellegrino
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引用次数: 0

Abstract

This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three-dimensional Heisenberg group, equipped with any of its left-invariant Lorentzian metrics. We prove that with the obvious exception of the flat case, no totally umbilical surfaces occur. On the other hand, we determine and explicitly describe several examples of minimal and constant mean curvature (CMC) surfaces.

洛伦兹海森堡群的完全脐面和极小面
这篇论文有多方面的目的。我们首先介绍了洛伦兹环境空间的子流形(类空间和类时间)的高斯映射的描述,并将曲面的高斯映射的一致性与总脐性和极小性联系起来。然后,我们将重点放在三维海森堡群的表面上,它配备了任意一个左不变洛伦兹度量。我们证明,除了明显的平坦情况,没有完全脐带表面发生。另一方面,我们确定并明确描述了几个例子的最小和恒定平均曲率(CMC)曲面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
157
审稿时长
4-8 weeks
期刊介绍: Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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