The study of moduli space and Teichmüller space has a long history. These two spaces lie in the intersections of the researches in many areas of mathematics and physics. Many deep results have been obtained in history by many famous mathematicians. Here we will only mention a few that are closely related to our discussions. Riemann was the first who considered the space M of all complex structu...

We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painlevé-Gullstrand form of the spacetime metric, whereas the data of the Randers problem ar...

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsi...

In this paper, we study the Finsler space with special (α, β)-metric is scalar flag curvature and proved that, if it weakly Berwald only vanishes curvature. Further, found that metric locally Minkowskian.

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We find an equation that characterizes Douglas metrics on a manifold of dimension n ≥ 3.

A criterion for a spacelike hypersurface in a conformally stationary spacetime to be a Cauchy hypersurface is given. The criterion is based on the forward and the backward completeness of a non-reversible Finsler metric associated to the hypersurface.

The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...