New applications of the Ahlfors Laplacian: Ricci almost solitons and general relativistic vacuum constraint equations

IF 1.2 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2025-03-01 Epub Date: 2024-12-27 DOI:10.1016/j.geomphys.2024.105414

Josef Mikeš , Sergey Stepanov , Irina Tsyganok

引用次数: 0

Abstract

In present article, we consider a

L^{2}

-orthogonal decomposition of the traceless part of the Ricci tensor of a closed Riemannian manifold and study its application to the geometry of compact Ricci almost solitons. In addition, we consider a

L^{2}

-orthogonal expansion of the traceless part of the second fundamental form of a closed spacelike hypersurface in a Lorentzian manifold and study its application to the problem of constructing solutions of general relativistic vacuum constraint equations. In these two cases, we use the well-known Ahlfors Laplacian.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

alhfors Laplacian的新应用：Ricci几乎孤子和广义相对论真空约束方程

本文考虑了闭黎曼流形的Ricci张量的无迹部分的l2 -正交分解，并研究了它在紧致Ricci几乎孤子几何中的应用。此外，我们考虑了洛伦兹流形中闭类空间超曲面第二基本形式的无迹部分的l2 -正交展开式，并研究了它在广义相对论真空约束方程解的构造问题中的应用。在这两种情况下，我们使用著名的阿尔弗斯拉普拉斯式。

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分钟内获得全文去求助

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

期刊最新文献

Constraints of the DΔKP hierarchy to the semi-discrete AKNS and Burgers hierarchies Rational first integrals and relative Killing tensors Polyhedral realizations for crystal bases and Young walls of classical affine types Conservation laws and cohomological intersections Geometric structures of anti-pre-Lie algebras