Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume...

The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of p...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.

The paper generalises Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. Additionally, in the rational case, the resulting distance is filtering invariant and can be computed efficiently.

We study the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza–Klein type) spaces. The problem of definition of spinors on generalized Finsler spaces is solved in the framework of the geometry of Clifford ...

‎based on a definition for circle in finsler space‎, ‎recently proposed by one of the present authors and z‎. ‎shen‎, ‎a natural definition of extrinsic sphere in finsler geometry is given and it is shown that a connected submanifold of a finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

We determine a 2-codimensional CR-structure on the slit tangent bundle T0M of a Finsler manifold (M, F) by imposing a condition on the almost complex structure associated to F when restricted to the structural distribution of a framed f -structure. This condition is satisfied when (M, F) is of scalar flag curvature (particularly flat). In the Riemannian case (M, g) this last condition means tha...

Let M be a differentiable manifold, T x its tangent space at ε and TM={(x,y);x M; y M} bundle. A C 0 -Finsler structure is continuous function F:TM → [0, ∞ ) such that F(x, · ):T an asymmetric norm. In this work we introduce the Pontryagin type structures, which are structures satisfy minimum requirements of Pontryagin's maximum principle for problem minimizing paths. We define extended geodesi...

In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.