Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector
Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector
复制标题
具有零平均曲率向量的洛伦兹 4 流形表面的各向同性
DOI：
10.1007/s12188-021-00254-y
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发表时间：
2022
影响因子：
0.4
通讯作者：
Ando Naoya
中科院分区：
文献类型：
--
作者：
Kei Kondo;Minoru Tanaka;酒井高司;Ando Naoya
我们已经有了黎曼4-流形中极小曲面和中立型4-流形中平均曲率向量为零的类空或类时曲面的各向同性的概念。本文基于对它的理解，定义并研究了零中曲率向量洛伦兹4-流形N中类空曲面或类时曲面的各向同性。如果曲面是类空间的，则各向同性意味着该曲面具有类光或零秒基本形式，或者它类似于Kähler曲面中的复杂曲线。此外，如果N是一种空间形式，则各向同性意味着该曲面具有这两个性质。如果曲面是类时间的，并且是一种空间形式，则各向同性意味着该曲面是完全测地线的。
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-manifoldNwith 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, ifNis a space form, then the isotropicity means that the surface has both the properties. If the surface is time-like and ifNis a space form, then the isotropicity means that the surface is totally geodesic.