四维中jacobi正交与Osserman条件的等价性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-22 DOI:10.1016/j.geomphys.2025.105599

Vladica Andrejić

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引用次数: 0

摘要

一个（可能不确定的）标量积空间上的代数曲率张量是雅可比正交的，当对于任何相互正交的向量X和Y，作用于Y的雅可比算子与作用于X的雅可比算子正交时，我们证明任何四维代数曲率张量是雅可比正交的当且仅当它是Osserman的。

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Equivalence between Jacobi-orthogonality and Osserman condition in dimension four

An algebraic curvature tensor on a (possibly indefinite) scalar product space is said to be Jacobi-orthogonal if, for any mutually orthogonal vectors X and Y, the Jacobi operator of X applied to Y is orthogonal to the Jacobi operator of Y applied to X. We prove that any four-dimensional algebraic curvature tensor is Jacobi-orthogonal if and only if it is Osserman.

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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