The book “Handbook of Finsler geometry” has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein’s vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the o...

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...

In this paper, we consider an autonomous two-dimensional ODE Kolmogorov-type system with three parameters, which is a particular of the general predator–prey systems Holling type II. By reformulating as set two second-order differential equations, investigate nonlinear dynamics from Jacobi stability point view using Kosambi–Cartan–Chern (KCC) geometric theory. We then determine connection, Berw...

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connectio...

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...

Randers manifolds are studied in the framework of the pullback bundle formalism, with the aid of intrinsic methods only. After checking a sufficient condition for a Randers manifold to be a Finsler manifold, we provide a systematic description of the Riemann-Finsler metric, the canonical spray, the Barthel endomorphism, the Berwald connection, the Cartan tensors and the Cartan vector field in t...

We investigate whether inflation, either isotropic or anisotropic, may be supported by n-forms. Canonical field strengths and their duals are taken into account, and they are allowed to have a potential and also, when necessary for slow-roll, a nonminimal curvature coupling. New isotropic solutions are found for three-forms. It is also shown that some n-form actions are equivalent to f(R) gravi...