Algebraic properties of Riemannian manifolds

被引：0
作者：
Youngjoo Chung
Chi-Ok Hwang
Hyun Seok Yang
机构：
[1] Gwangju Institute of Science and Technology,School of Electrical Engineering and Computer Science
[2] Gwangju Institute of Science and Technology,Division of Liberal Arts and Sciences
[3] Gwangju Institute of Science and Technology,Department of Physics and Photon Science
来源：
General Relativity and Gravitation | 2023年 / 55卷
关键词：
Riemannian manifolds; Curvature invariants; Algebraic identities of Riemann tensors;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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共 90 条
[21]  
MacCallum MAH(1972)Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space Stud. Appl. Math. 51 1031-undefined
[22]  
Martín-García JM(1981)The identities of the algebraic invariants of the four-dimensional Riemann tensor J. Math. Phys. 22 3135-undefined
[23]  
Portugal R(1986)A Complete Set of Riemann Invariants Class. Quantum Grav. 3 1059-undefined
[24]  
Manssur LRU(1991)A new spinor identity and the vanishing of certain Riemann tensor invariants J. Math. Phys. 32 539-undefined
[25]  
Haskins CN(1996)Normal forms for tensor polynomials: I. The Riemann tensor J. Math. Phys. 37 653-undefined
[26]  
Narlikar VV(1997)Einstein manifolds as Yang-Mills instantons General Relat. Grav. 29 1151-undefined
[27]  
Karmarkar KR(1998)Yang-Mills instantons from gravitational instantons General Relat. Grav. 30 1350097-undefined
[28]  
Harvey A(1992)An efficient representation of Euclidean gravity I Class. Quantum Grav. 9 087-undefined
[29]  
Géhéniau J(2013)Anatomy of Einstein manifolds Mod. Phys. Lett. A 28 025-undefined
[30]  
Debever R(2011)Self-duality in four-dimensional Riemannian geometry JHEP 04 425-undefined
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