Let x : (M, F ) →֒ (V n+1, F ) be a simply connected hypersurface in a Minkowski space (V n+1, F ). In this paper, using the Gauss formula of Chern connection on Finsler submanifolds, we shall prove that if x(p) is normal to Tp(M)(∀p ∈ M), then M with the induced metric is isometric to the standard Euclidean sphere.

We generalize the Zermelo navigation on Riemannian manifolds (M,h), admitting a space dependence of a ship's speed 0 < |u(x)|h ≤ 1 in the presence of a perturbation W̃ determined by a strong (critical) velocity vector eld satisfying |W̃ (x)|h = |u(x)|h, with application of Finsler metric of Kropina type.

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 paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: L(x, y) −→ L(x, y) = f(eL(x, y), β(x, y)). This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated g...

It is proved that all invariant functions of a complex Finsler manifold can be totally recovered from the torsion and curvature of the connection introduced by Kobayashi for holomorphic vector bundles with complex Finsler structures. Equations of the geodesics and Jacobi fields of a generic complex Finsler manifold, expressed by means Kobayashi’s connection, are also derived.

We begin the study of billiard dynamics in Finsler geometry. We deduce the Finsler billiard reflection law from the “least action principle”, and extend the basic properties of Riemannian and Euclidean billiards to the Finsler and Minkowski settings, respectively. We prove that the Finsler billiard map is a symplectomorphism, and compute the mean free path of the Finsler billiard ball. For the ...

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F ). To this end...

Some problems concerning to Liouville distribution and framed f -structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

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.

The characterization of Finsler spaces of constant curvature is an old and cumbersome one. In the present paper we obtain the conditions for a Kropina space to be of constant curvature improving in this way the characterization given by Matsumoto ([6]) as well as our past results ([13]). M.S.C. 2010: 58B20, 53B21.