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 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...

Nonadditive measure is a generalization of additive probability measure. Sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. Integral inequalities play important roles in classical probability and measure theory. The classical Berwald integral inequality is one of the famous inequalities. This inequality turns out to have ...

Berwald geometries are Finsler close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which given Lagrangian has satisfy be of type. Applied $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces condition for the Levi-Civita covariant derivative defining $1$-form. illustrate...

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...

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox?We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

The aim of this work is to show a Berwald type inequality for the extremal universal integrals based on (α ,m) concave function. Some examples are given to illustrate the validity of these inequalities.