We model pseudo–Finsler geometries, with pseudo–Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo–Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field eq...

In the present paper, we investigate the necessary and sufficient condition of a given Finsler metric to be Einstein. The considered Einstein Finsler metric in the study describes all different kinds of Einstein metrics which are pointwise projective to the given one.

We formulate a statistical analogy of regular Lagrange mechanics and Finsler geometry derived from Grisha Perelman’s functionals and generalized for nonholonomic Ricci flows. Explicit constructions are elaborated when nonholonomically constrained flows of Riemann metrics result in Finsler like configurations, and inversely, when geometric mechanics is modelled on Riemann spaces with a preferred...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...