Biharmonic submanifolds of the quaternionic projective space

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-09-04 DOI:10.1016/j.geomphys.2024.105310

Clebes Brandão

引用次数: 0

Abstract

The present paper is devoted to the study of biharmonic submanifolds in quaternionic space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We study biharmonic submanifolds with parallel mean curvature and biharmonic submanifolds which are pseudo-umbilical in the quaternionic projective space. We find the relation between the bitension field of the inclusion of a submanifold in the n-dimensional quaternionic projective space and the bitension field of the inclusion of the corresponding Hopf-tube in the unit sphere of dimension 4n+3.

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四元投影空间的双谐波子平面

本文致力于研究四元数空间形式中的双谐波子线面。在给出这些空间中子曲率的双谐波条件之后，我们研究了不同的特殊情况，并获得了曲率估计值。我们研究了在四元投影空间中具有平行平均曲率的双谐波子曼形体和伪伞形的双谐波子曼形体。我们发现了在 n 维四元投影空间中包含子曼形体的位张场与在 4n+3 维单位球中包含相应霍普夫管的位张场之间的关系。

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

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