Let Fm = (M,F ) be a Finsler manifold and G be the Sasaki– Finsler metric on the slit tangent bundle TM0 = TM {0} of M . We express the scalar curvature ρ̃ of the Riemannian manifold (TM0, G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ̃ to be a positively homogenenous function of degree zero with respect to the fiber coo...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

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 this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

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...

the general relatively isotropic mean landsberg metrics contain the general relativelyisotropic landsberg metrics. a class of finsler metrics is given, in which the mentioned two conceptsare equivalent. in this paper, an interpretation of general relatively isotropic mean landsberg metrics isfound by using c-conformal transformations. some necessary conditions for a general relativelyisotropic ...

The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β)-metrics defined by a Riemannian metric α and an 1-form β, represent an important class of Finsler metrics, which contains the Matsumoto metric. In this paper, we study and characterize locally dually flat first approximation of the Matsumoto metric with isotropic S-curvature, which is not ...

David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm of a tangent vector from the distance f...

We develop the method of anholonomic frames with associated nonlinear connec-tion (in brief, N–connection) structure and show explicitly how geometries with lo-cal anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton geometry) can bemodeled in the metric–affine spaces. There are formulated the criteria when such gen-eralized Finsler metrics are effectively induced in the...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.