The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza– Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on highe...

A generalization of Finsler structures on surfaces is proposed and the differential invariants of such structures are developed. The information obtained is then used to construct examples of Finsler structures and generalized Finsler structures which satisfy various interesting curvature conditions. In particular, examples are constructed of non-Riemannian Finsler structures on the 2-sphere wh...

The curvature characteristics of particular classes Finsler spaces, such as homogeneous are one the major issues in geometry. In this paper, we have obtained expression for S-curvature space with a generalized Matsumoto metric and demonstrated that isotropic has to vanish S-curvature. We also derived mean Berwald by using formula

Every Riemannian metric or Finsler on a manifold induces spray via its geodesics. In this paper, we discuss several expressions for the [Formula: see text]-curvature of spray. We show that sprays obtained by projective deformation using S-curvature always have vanishing text]-curvature. Then establish Beltrami Theorem with text].

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...

We consider the global well-posedness of weak energy conservative solution to a general quasilinear wave equation through variational principle, where may form finite time cusp singularity, when concentrates. As main result in this paper, we construct Finsler type optimal transport metric, then prove that flow is Lipschitz under metric. also generic regularity by applying Thom's transversality ...