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–Lag...

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen et al. [Internat. J. Math. 29 (2018), 1850081], with another “warping”, one that is consistent static spacetimes. We will give PDE characterization for proposed to be Ricci-flat and explicitly construct two non-Riemannian examples.

In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known proven the Randers Indeed, that every connected space with non-positive flag curvature and isotropic S-curvature is Riemannian or locally Minkowskian. We extend Szabó's theorem Berwald surfaces show metrics are second to (α,β)-metr...