Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

Details Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics

2008-06-24

arxiv.org/abs/0806.3810v2

SIGMA 4:071,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

This is a contribution to the Special Issue "Elie Cartan and Differential Geometry", published in SIGMA (Symmetry, Integrabili

Scientific paper

10.3842/SIGMA.2008.071

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.

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