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Symmetry inheritance in Riemannian manifolds with physical applications

Symmetry inheritance in Riemannian manifolds with physical applications We study Riemannian manifolds, subject to a prescribed symmetry inheritance, defined by LξΩ=2αΩ, where Ω, ga, and Lξ are geometric/physical object, function, and Lie derivative operator with respect to a vector field ξ. In this paper, we set Ω=Riemann curvature tensor or Ricci tensor and obtain several new results relevant to physically significant material curves, proper conformai and proper nonconformal symmetries. In particular, we concentrate on a time-like Ricci inheritance vector parallel to the velocity vector of a perfect fluid spaced me. We claim new and physically relevant equations of state. All key results are supported by physical examples, including the Friedman-Robertson-Walker universe models. In general, this paper opens a new area of research on symmetry inheritance with a potential for further applications in mathematical physics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Symmetry inheritance in Riemannian manifolds with physical applications

Duggal, K.
Acta Applicandae Mathematicae , Volume 31 (3) – Jan 3, 2005
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References (27)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00997119
Publisher site
See Article on Publisher Site

Abstract

We study Riemannian manifolds, subject to a prescribed symmetry inheritance, defined by LξΩ=2αΩ, where Ω, ga, and Lξ are geometric/physical object, function, and Lie derivative operator with respect to a vector field ξ. In this paper, we set Ω=Riemann curvature tensor or Ricci tensor and obtain several new results relevant to physically significant material curves, proper conformai and proper nonconformal symmetries. In particular, we concentrate on a time-like Ricci inheritance vector parallel to the velocity vector of a perfect fluid spaced me. We claim new and physically relevant equations of state. All key results are supported by physical examples, including the Friedman-Robertson-Walker universe models. In general, this paper opens a new area of research on symmetry inheritance with a potential for further applications in mathematical physics.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jan 3, 2005

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