Levi-flat real hypersurfaces in nonflat complex planes

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-06-28 DOI:10.1016/j.geomphys.2024.105259

Yaning Wang, Yuan Zhou

引用次数: 0

Abstract

Let M be a non-ruled weakly 2-Hopf real hypersurface in a nonflat complex plane whose mean curvature is invariant along the Reeb flow. In this paper, it is proved that M is Levi-flat if and only if M is locally congruent to a strongly 2-Hopf real hypersurface of a special type. As a corollary we present a class of non-ruled Levi-flat real hypersurfaces of dimension three with non-constant mean curvature.

查看原文本刊更多论文

非平面复平面中的列维平实超曲面

设 M 是非平面复平面中的非规则弱 2-Hopf 实超曲面，其平均曲率沿 Reeb 流不变。本文证明，当且仅当 M 与一个特殊类型的强 2-Hopf 实超曲面局部全等时，M 才是 Levi 平面。作为推论，我们提出了一类具有非恒定平均曲率的三维非规则列维平坦实超曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity