Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Abstract

We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart-Moffat and Finsler-Lagrange spaces with connections compatible to a general nonsymmetric metric structure. Elaborating a metrization procedure for arbitrary distinguished connections, we define the class of distinguished linear connections which are compatible with the nonlinear connection and general nonsymmetric metric structures. The nonsymmetric gravity theory is formulated in terms of metric compatible connections. Finally, there are constructed such nonholonomic deformations of geometric structures when the Einstein and/or Lagrange-Finsler manifolds are transformed equivalently into spaces with generic local anisotropy induced by nonsymmetric metrics and generalized connections. We speculate on possible applications of such geometric methods in Einstein and generalized theories of gravity, analogous gravity and geometric mechanics.

This is a contribution to the Special Issue "Elie Cartan and Differential Geometry", published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

References in corpus (11)

• Testing modified gravity with globular cluster velocity dispersions
• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
• The cosmology of the nonsymmetric theory of gravitation
• Einstein Gravity in Almost Kahler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics
• Nonholonomic Ricci Flows and Parametric Deformations of the Solitonic pp--Waves and Schwarzschild Solutions
• Nonholonomic Ricci Flows: I. Riemann Metrics and Lagrange-Finsler Geometry
• Nonholonomic Ricci Flows: Exact Solutions and Gravity
• Nonholonomic Ricci Flows and Running Cosmological Constant: 3D Taub-NUT Metrics

Cited by in corpus (1)

• Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics