In this paper we have studied the class of Finsler metrics, called C3-like metrics which satisfy un-normal and normal Ricci flow equation and
 proved that such are Einstein.

We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschild-de Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of Λ. We explain why this does not imply that lensing phenomena are independent of Λ. Motivated by this example, we find a large collection of one-parameter fami...

in this paper, we study projective randers change and c-conformal change of p-reduciblemetrics. then we show that every p-reducible generalized landsberg metric of dimension n  2 must be alandsberg metric. this implies that on randers manifolds the notions of generalized landsberg metric andberwald metric are equivalent.

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo–Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions w...

In 1984 C.Shibata has dealt with a change of Finsler metric which is called a β-change of metric [12]. For a β-change of Finsler metric, the differential oneform β play very important roles. In 1985 M.Matsumoto studied the theory of Finslerian hypersurfaces [6]. In there various types of Finslerian hypersurfaces are treated and they are called a hyperplane of the 1st kind, a hyperplane of the 2...

A complex Finsler metric is an upper semicontinuous function F : T 1,0 M → R + defined on the holomorphic tangent bundle of a complex Finsler manifold M , with the property that F (p; ζv) = |ζ|F (p; v) for any (p; v) ∈ T 1,0 M and ζ ∈ C. Complex Finsler metrics do occur naturally in function theory of several variables. The Kobayashi metric introduced in 1967 ([K1]) and its companion the Carath...

In Theorem 1, we generalize the results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwa...

Control Contraction Metrics (CCMs) provide a nonlinear controller design involving an offline search for a Riemannian metric and an online search for a shortest path between the current and desired trajectories. In this paper, we generalize CCMs to Finsler geometry, allowing the use of nonRiemannian metrics. We provide open loop and sampled data controllers. The sampled data control constructio...

We obtain some results in both, Lorentz and Finsler geometries, by using a correspondence between the conformal structure of standard stationary spacetimes on M = R × S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization on when R×S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface),...