In this paper we study spherically symmetric metrics on a space in $\mathbb{R}^n$ with scalar and constant flag curvature also obtain families of type metrics. Many explicit examples are provided for Douglas curvature. Furthermore, new projectively flat Finsler given. We provide family which not type.

in this paper, applying the concept of generalized a-valued norm on a right h  - module and also the notion of ϕ-homomorphism of finsler modules over c  -algebras we rst improve the denition of the finsler module over h  -algebra and then dene ϕ-morphism of finsler modules over h  -algebras. finally we present some results concerning these new ones.

We present a gravitational quantum dynamics theory that combines field for particle in space-time with classical Einstein’s general relativity non-Riemannian Finsler space. This approach is based on the geometrization of mechanics proposed Tavernelli (Ann. Phys. 371:239, 2016) and effects into global curvature space induced by potential associated to matter fields. In order make this compatible...

This paper is a continuation of the second author’s previous work [Internat. J. Math. 30 (2019)]. We investigate isoperimetric problem in 2-dimensional Finsler space form ...

Let $$M=S^n/ \Gamma $$ and h be a nontrivial element of finite order p in $$\pi _1(M)$$ , where the integer $$n, p\ge 2$$ $$\Gamma is abelian group which acts freely isometrically on n-sphere therefore M diffeomorphic to compact space form. In this paper, we prove that for every irreversible Finsler form (M, F) with reversibility $$\lambda flag curvature K satisfying $$\begin{aligned} \frac{4p^...

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

The work extends the A. Connes’ noncommutative geometry to spaces with generic local anisotropy. We apply the E. Cartan’s anholonomic frame approach to geometry models and physical theories and develop the nonlinear connection formalism for projective module spaces. Examples of noncommutative generation of anholonomic Riemann, Finsler and Lagrange spaces are analyzed. We also present a research...