We study the cylindrical symmetric Finsler metrics. obtain system of differential equations such metrics which are projectively flat. give a family solutions this system. Examples included.

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...

If D is a bounded convex domain in C , then the work of Lempert [L] and Royden-Wong [RW] (see also [A]) show that given any point p ∈ D and any non-zero tangent vector v ∈ C at p, there exists a holomorphic map φ:U → D from the unit disk U ⊂ C into D passing through p and tangent to v in p which is an isometry with respect to the hyperbolic distance of U and the Kobayashi distance of D. Further...

We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski–Demianski metrics one obtains a family of local toric Kähler–Einstein metrics. These can be used to construct local Sasaki–Einstein metrics in five dimensions, which are generalisations of the Y p,q metrics. In fact, we find that the local metrics are diffeomorphic to those recently found by Cvetic, Lu, Page...

The paper establishes that a generalization of Monge–Kantorovich equation gives rise to necessary and sufficient optimality condition for the Kantorovich dual problem minimal flow associated with very degenerate Finsler metric without any assumption on coerciveness.