Lie symmetries of geodesic equations and projective collineations

被引：19

作者：

Tsamparlis, Michael ^{[1
]}

Paliathanasis, Andronikos ^{[1
]}

机构：

[1] Univ Athens, Dept Phys, Sect Astron Astrophys Mech, Athens 15783, Greece

来源：

NONLINEAR DYNAMICS | 2010年 / 62卷 / 1-2期

关键词：

Geodesics; General relativity theory; Classical mechanics; Collineations; Riemannian space; Autoparallels; Lie symmetries; Projective collineations; DIFFERENTIAL-EQUATIONS; SPACES;

D O I：

10.1007/s11071-010-9710-x

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

We prove a theorem which relates the Lie symmetries of the geodesic equations in a Riemannian space with the collineations of the metric. We apply the results to Einstein spaces and spaces of constant curvature. Finally with examples we show the use of the results.

引用

页码：203 / 214

页数：12

共 50 条

[41] Collineations in a finite projective geometry
Veblen, Oswald
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1907, 8 (1-4) : 366 - 368
[42] Symmetries of the Painleve equations and the connection with projective differential geometry
Bordag, L
EUROPEAN WOMEN IN MATHEMATICS, 1999, : 145 - 159
[43] Rational first integrals of geodesic equations and generalised hidden symmetries
Aoki, Arata
Houri, Tsuyoshi
Tomoda, Kentaro
CLASSICAL AND QUANTUM GRAVITY, 2016, 33 (19)
[44] Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric
Kara, A. H.
Mahomed, F. M.
Qadir, Asghar
NONLINEAR DYNAMICS, 2008, 51 (1-2) : 183 - 188
[45] The connection between isometries and symmetries of geodesic equations of the underlying spaces
Feroze, Tooba
Mahomed, F. M.
Qadir, Asghar
NONLINEAR DYNAMICS, 2006, 45 (1-2) : 65 - 74
[46] Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric
A. H. Kara
F. M. Mahomed
Asghar Qadir
Nonlinear Dynamics, 2008, 51 : 183 - 188
[47] The Connection Between Isometries and Symmetries of Geodesic Equations of the Underlying Spaces
Tooba Feroze
F. M. Mahomed
Asghar Qadir
Nonlinear Dynamics, 2006, 45 : 65 - 74
[48] APPLICATIONS OF LIE DERIVATIVES TO SYMMETRIES, GEODESIC MAPPINGS, AND FIRST INTEGRALS IN RIEMANNIAN SPACES
KATZIN, GH
LEVINE, J
COLLOQUIUM MATHEMATICUM, 1972, 26 : 21 - 38
[49] PROJECTIVE COLLINEATIONS IN EINSTEIN-SPACES
BARNES, A
CLASSICAL AND QUANTUM GRAVITY, 1993, 10 (06) : 1139 - 1145
[50] Lie Point Symmetries of Differential-Difference Equations
DING Wei~1 TANG Xiao-Yan~(2
Communications in Theoretical Physics, 2004, 41 (05) : 645 - 648

← 1 2 3 4 5 →