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...

In this paper, we study the curvature features of class homogeneous Randers metrics. For these metrics, first find a reduction criterion to be Berwald metric based on mild restriction their Ricci tensors. Then, prove that every with relatively isotropic (or weak) Landsberg must Riemannian. This provides an extension well-known Deng-Hu theorem proves same result for Berwald-Randers non-zero flag...

We determine a 2-codimensional CR-structure on the slit tangent bundle T0M of a Finsler manifold (M, F) by imposing a condition on the almost complex structure associated to F when restricted to the structural distribution of a framed f -structure. This condition is satisfied when (M, F) is of scalar flag curvature (particularly flat). In the Riemannian case (M, g) this last condition means tha...

In this paper, we introduce isoparametric functions and hypersurfaces in conic Finsler spaces. We find that there are probably other Minkowski spaces besides the hyperplanes, hyperspheres cylinders, such as helicoids. Moreover, give a complete classification of Kropina with constant flag curvature.

In this work, we continue with the classification for positively curved homogeneous Finsler spaces (G/H,F ). With the assumption that the homogeneous space G/H is odd dimensional and the positively curved metric F is reversible, we only need to consider the most difficult case left, i.e. when the isotropy group H is regular in G. Applying the fixed point set technique and the homogeneous flag c...

The well-known Funk metric F (x, y) is projectively flat with constant flag curvature K = −1/4 and the Hilbert metric Fh(x, y) := (F (x, y) + F (x,−y))/2 is projectively flat with constant curvature K = −1. These metrics are the special solutions to Hilbert’s Fourth Problem. In this paper, we construct a non-trivial R-flat spray using the Funk metric. It is then an inverse problem in the calcul...

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.