Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity

TL;DR

This work explores advanced geometric structures like Riemann-Cartan and Finsler geometries, applying anholonomic frames to construct solutions in gravity and mechanics, including black holes, wormholes, and solitons, with implications for noncommutative geometry.

Contribution

It develops methods for constructing and analyzing solutions with complex geometric structures in gravity and mechanics, including noncommutative extensions and stability analysis.

Findings

Constructed off-diagonal exact solutions with torsion and nonmetricity.

Classified Lagrange and Finsler affine spaces.

Defined nonholonomic Dirac operators for applications in geometry.

Abstract

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.