Lagrange geometry via complex Lagrange geometry.
Lagrange spaces with indicatrices as constant mean curvature surfaces or minimal surfaces.
Lagrange spaces with -metric.
Lagrangians and higher order tangent spaces.
Les géométries de Hilbert sont à géométrie locale bornée
On montre que la géométrie de Hilbert d’un domaine convexe de est à géométrie locale bornée c-à-d que pour un rayon fixé, toutes les boules sont bilipschitz à un domaine de euclidien. On en déduit que si la géométrie de Hilbert est hyperbolique au sens de Gromov, alors le bas de son spectre est strictement positif. On donne un contre-exemple en dimension trois qui montre que la réciproque n’est pas vraie pour les géométries de Hilbert non planes.
Linear connections compatible with the -structure on the Lagrangian spaces.
Linear Connections Compatible With the F(3,1)-structure on the Lagrangian Space
Local invariants of a pseudo-Riemannian manifold.
Metric Entropy of Homogeneous Spaces
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Metric semi-symmetric -linear connections in the bundle of accelerations.
Metrische Zusammenhänge und Torsion bei einfachen p-Vektoren.
Metrizability of affine connections.
Metrizability of affine connections.
Minimal submanifolds in general (α,β)-spaces
The volume forms of general (α,β)-metrics are studied. Some equations for minimal submanifolds in general (α,β)-spaces are established by using the normal frame field, and some minimal surfaces in general (α,β)-spaces with special curvature properties are constructed.
Multiplicity and stability of closed geodesics on Finsler 2-spheres
A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.
Naturally reductive homogeneous -metric spaces
In the present paper we study naturally reductive homogeneous -metric spaces. We show that for homogeneous -metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous -metric spaces.
Nonholonomic frames in Finsler geometry.
Nonlinear connections and spinor geometry.
Notes on new Finsler metric function.
On Asymmetric Distances
In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the...