平均曲率矢量为零的洛伦兹4流形中曲面的各向同性

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-03 DOI:10.1007/s12188-021-00254-y

Naoya Ando

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引用次数: 3

摘要

我们已经有了黎曼4流形中最小曲面和中性4流形中平均曲率为零的类空或类时曲面的各向同性的概念。本文在对其理解的基础上，定义并研究了平均曲率矢量为零的洛伦兹4流形N中类空曲面或类时曲面的各向同性。如果表面是类空间的，那么各向同性意味着表面具有类光或零秒基本形式，或者它是Kähler表面中复杂曲线的模拟。另外，如果N是一种空间形式，那么各向同性意味着表面具有这两种性质。如果表面是类时的，如果N是空间形式，那么各向同性意味着表面完全是测地线。

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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Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector

We already have the concept of isotropicity of a minimal surface in a Riemannian 4-manifold and a space-like or time-like surface in a neutral 4-manifold with zero mean curvature vector. In this paper, based on the understanding of it, we define and study isotropicity of a space-like or time-like surface in a Lorentzian 4-manifold N with zero mean curvature vector. If the surface is space-like, then the isotropicity means either the surface has light-like or zero second fundamental form or it is an analogue of complex curves in Kähler surfaces. In addition, if N is a space form, then the isotropicity means that the surface has both the properties. If the surface is time-like and if N is a space form, then the isotropicity means that the surface is totally geodesic.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.