Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

• Main Authors: Vacaru, S, Stavrinos, P, Gaburov, E, Gonţa, D
• Format: Journal Article
• Language: English
• Published: 06.08.2005
• Subjects: Mathematics - Differential Geometry; Mathematics - Mathematical Physics; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Theory; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.gr-qc/0508023

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