On the Chern–weil Homomorphism in Finsler Spaces

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

A structure by conformal transformations of Finsler functions on the projectivised tangent bundle of Finsler spaces with the Chern connection

It is shown that the projectivised tangent bundle of Finsler spaces with the Chern connection has a contact metric structure under a conformal transformation with certain condition of the Finsler function and moreover it is locally isometric to E × Sm−1(4) for m > 2 and flat for m = 2 if and only if the Cartan tensor vanishes, i.e., the Finsler space is a Riemannian manifold. M.S.C. 2000: 53C60...

Non Commutative Chern - Weil Homomorphism

Finsler Connections in Generalized Lagrange Spaces

The Chern–Rund connection from Finsler geometry is settled in the generalized Lagrange spaces. For the geometry of these spaces, we refer to [5]. Mathematics Subject Classification: 53C60

A generalization of the holomorphic flag curvature of complex Finsler spaces

The notion of holomorphic bi-flag curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is devoted to obtain the characterizations of the holomorphic bi-flag curvature. For the class of generalized...