a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

using the electrostatic capacity of a condenser, the existence of a distance function on a finsler space is discussed. this distance function divides finsler spaces into the two classes, denoted here by i and ii. the topology generated by this distance on the finsler spaces of class ii coincides with its intrinsic topology. this work provides a natural extension of mathematical analysis tools n...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C Finsler manifold M is determined by the normed algebra C b (M) of all real-valued, bounded and C k smooth functions with bounded derivative defined on M . As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C Finsler manifold M is determined by the algebra...

In this note the geometry of the indicatrix (I, L̃) is studied as a hypersurface of a complex Finsler space (M,L). The induced Chern-Finsler and Berwald connections are defined and studied. The induced Berwald connection coincides with the intrinsic Berwald connection of the indicatrix bundle. We considered a special projection of a geodesic curve on a complex Finsler space (M,L), called the ind...

The notion of holomorphic bi-flag curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is devoted to obtain the characterizations of the holomorphic bi-flag curvature. For the class of generalized...

Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding maps to Banach spaces of L∞-type are developed and generalized. For every Finsler volume functional (such as the Busemann volume or the Holmes– Thompson volume), a natural extension is constructed from the class of Finsler metrics to all Lipschitz metrics, and the notion of area is defined for Lipschitz surface...

A Finsler space (M,Σ) is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason [13], it is shown that a geodesically reversible Finsler metric of constant flag curvature on the...

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.