Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

Details Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

2005-08-06

arxiv.org/abs/gr-qc/0508023v2

Differential Geometry -- Dynamical Systems, Monograph #7 (Geometry Balkan Press, 2006) http://www.mathem.pub.ro/dgds/mono/va-t

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Accepted by Geometry Balkan Press, 693 pages + 3 eps figures, version 2 with minor modifications, new affiliation and Preface

Scientific paper

The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries and Clifford structures modelled on such manifolds. The choice of material presented has evolved from various applications in modern gravity and geometric mechanics and certain generalizations to noncommutative Riemann-Finsler geometry. The authors develop and use the method of anholonomic frames with associated nonlinear connection structure and apply it to a number of concrete problems: constructing of generic off-diagonal exact solutions, in general, with nontrivial torsion and nonmetricity, possessing noncommutative symmetries and describing black ellipsoid/torus configurations, locally anisotropic wormholes, gravitational solitons and warped factors and investigation of stability of such solutions; classification of Lagrange/ Finsler -- affine spaces; definition of nonholonomic Dirac operators and their applications in commutative and noncommutative Finsler geometry.

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