Ricci Solitons on Riemannian Hypersurfaces Arising from Closed Conformal Vector Fields in Riemannian and Lorentzian Manifolds

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Norah Alshehri, Mohammed Guediri
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引用次数: 0

Abstract

This paper investigates Ricci solitons on Riemannian hypersurfaces in both Riemannian and Lorentzian manifolds. We provide conditions under which a Riemannian hypersurface, exhibiting specific properties related to a closed conformal vector field of the ambiant manifold, forms a Ricci soliton structure. The characterization involves a delicate balance between geometric quantities and the behavior of the conformal vector field, particularly its tangential component. We extend the analysis to ambient manifolds with constant sectional curvature and establish that, under a simple condition, the hypersurface becomes totally umbilical, implying constant mean curvature and sectional curvature. For compact hypersurfaces, we further characterize the nature of the Ricci soliton.

黎曼超曲面上的黎奇孤子源自黎曼和洛伦兹方程中的封闭共形矢量场
本文研究了黎曼流形和洛伦兹流形中黎曼超曲面上的黎奇孤子。我们提供了一些条件,在这些条件下,表现出与环境流形的封闭共形向量场相关的特定性质的黎曼超曲面会形成黎奇孤子结构。这一特征涉及几何量与共形向量场行为(尤其是其切向分量)之间的微妙平衡。我们将分析扩展到具有恒定截面曲率的环境流形,并确定在一个简单的条件下,超曲面变得完全脐形,这意味着恒定的平均曲率和截面曲率。对于紧凑超曲面,我们进一步描述了利玛窦孤子的性质。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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