黎曼流形的代数性质

IF 2.1 4区物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS

General Relativity and Gravitation Pub Date : 2023-08-17 DOI:10.1007/s10714-023-03141-4

Youngjoo Chung, Chi-Ok Hwang, Hyun Seok Yang

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引用次数: 3

摘要

利用曲率张量的不可约分解，探讨了黎曼流形曲率张量的代数性质。该方法为分析不可约基提供了有力的工具，同时也为确定任意黎曼多项式的线性相关性提供了一种算法。我们完全指定了四次标量的13个独立基元，并明确地找到了26个标量不变量之间的13个线性关系。我们的方法提供了几个全新的结果，包括从90个五次标量中识别23个独立基元素的一些线索，这些线索很难找到。

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Algebraic properties of Riemannian manifolds

Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find 13 linear relations among 26 scalar invariants. Our method provides several completely new results, including some clues to identify 23 independent basis elements from 90 quintic scalars, that are difficult to find otherwise.

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来源期刊

General Relativity and Gravitation 物理-天文与天体物理

CiteScore

4.60

自引率

3.60%

发文量

136

审稿时长

3 months

期刊介绍： General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.