Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

The notion of holomorphic bisectional 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 emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

We obtain some results in both, Lorentz and Finsler geometries, by using a correspondence between the conformal structure of standard stationary spacetimes on M = R × S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization on when R×S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface),...

In this paper, we construct a framed f -structure on the slit tangent space of a Rizza manifold. This induces on the indicatrix bundle an almost contact metric. We find the conditions under which this structure reduces to a contact or to a Sasakian structure. Finally we study these structures on Kählerian Finsler manifolds. M.S.C. 2010: 53B40, 53C60, 32Q60, 53C15.

In this article, we review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Fin...

We survey some results in extending the Finsler geometry of the group of Hamil-tonian diffeomorphisms of a symplectic manifold, known as Hofer's geometry, to the space of Lagrangian embeddings. Our intent is to illustrate some ideas of this still developing field, rather then to be complete or comprehensive.

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers–Steenrod theorem and for the differentiability of Finslerian submetries. AMS Subject Class. (2010): 53B40