Symmetries in Riemann-Cartan Geometries

被引:0
|
作者
Mcnutt, David D. [1 ]
Coley, Alan A. [2 ]
Van Den Hoogen, Robert J. [3 ]
机构
[1] Polish Acad Sci, Ctr Theoret Phys, Warsaw, Poland
[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS, Canada
[3] St Francis Xavier Univ, Dept Math & Stat, Antigonish, NS, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
symmetry; Riemann-Cartan; frame formalism; local homogeneity; TORSION THEORIES;
D O I
10.3842/SIGMA.2024.078
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries. One notable difference, is the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.
引用
收藏
页数:20
相关论文
共 50 条
  • [31] Riemann-Cartan Geometry of Nonlinear Dislocation Mechanics
    Yavari, Arash
    Goriely, Alain
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 205 (01) : 59 - 118
  • [32] CONFORMAL AND AXIAL ANOMALIES IN RIEMANN-CARTAN SPACE
    KIMURA, T
    PROGRESS OF THEORETICAL PHYSICS, 1981, 66 (06): : 2011 - 2024
  • [33] Torsion structure in Riemann-Cartan manifold and dislocation
    Lee, X
    Baldo, M
    Duan, YS
    GENERAL RELATIVITY AND GRAVITATION, 2002, 34 (10) : 1569 - 1577
  • [34] An Entropy Functional for Riemann-Cartan Space-Times
    Hammad, F.
    INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2012, 51 (02) : 362 - 373
  • [35] SEELEY-DEWITT COEFFICIENTS IN A RIEMANN-CARTAN MANIFOLD
    COGNOLA, G
    ZERBINI, S
    PHYSICS LETTERS B, 1988, 214 (01) : 70 - 74
  • [36] Gravitational anomalies in higher dimensional Riemann-Cartan space
    Yajima, S.
    Tokuo, S.
    Fukuda, M.
    Higashida, Y.
    Kamo, Y.
    Kubota, S-I
    Taira, H.
    CLASSICAL AND QUANTUM GRAVITY, 2007, 24 (04) : 965 - 979
  • [37] Nonholonomic versus vakonomic dynamics on a Riemann-Cartan manifold
    Guo, YX
    Wang, Y
    Chee, GY
    Mei, FX
    JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (06)
  • [38] Riemann-Cartan space-time in stringy geometry
    Sazdovic, B
    MATHEMATICAL, THEORETICAL AND PHENOMENOLOGICAL CHALLENGES BEYOND THE STANDARD MODEL: PERSPECTIVES OF THE BALKAN COLLABORATIONS, 2005, : 94 - 108
  • [39] Vanishing theorems for some classes of Riemann-Cartan manifolds
    Gordeeva I.A.
    Journal of Mathematical Sciences, 2011, 177 (5) : 649 - 653
  • [40] BOSONIZATION IN A TWO-DIMENSIONAL RIEMANN-CARTAN GEOMETRY
    DENARDO, G
    SPALLUCCI, E
    NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-BASIC TOPICS IN PHYSICS, 1987, 98 (01): : 25 - 36