In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.

A generalization of Finsler structures on surfaces is proposed and the differential invariants of such structures are developed. The information obtained is then used to construct examples of Finsler structures and generalized Finsler structures which satisfy various interesting curvature conditions. In particular, examples are constructed of non-Riemannian Finsler structures on the 2-sphere wh...

The credit for introducing the geometry of Lagrange spaces and their subspaces goes to the famous Romanian geometer Miron 1 . He developed the theory of subspaces of a Lagrange space together with Bejancu 2 . Miron and Anastasiei 3 and Sakaguchi 4 studied the subspaces of generalized Lagrange spaces GL spaces in short . Antonelli and Hrimiuc 5, 6 introduced the concept of φ-Lagrangians and stud...

The geometries of higher order, defined in the present paper as the study of the category of jet bundles (J o M, π,M), were suggested by the old problem of the prolongations to J o M of Riemannian structures g apriori given on the base manifold M. In the case k = 1 there are very good examples: the geometry of Finsler spaces and the geometry of Lagrange spaces, [3]. For k > 1 there are some geo...

The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...

In this paper we study Banakh’s quarter-stratifiability among generalized ordered (GO)-spaces. All quarterstratifiable GO-spaces have a σ-closed-discrete dense set and therefore are perfect, and have a Gδ-diagonal. We characterize quarter-stratifiability among GO-spaces and show that, unlike the situation in general topological spaces, quarter-stratifiability is a hereditary property in GO-spac...

We extend the construction of Born’s Reciprocal Phase Space Relativity to the case of Clifford Spaces which involve the use of polyvectors and a lower/upper length scale. We present the generalized polyvector-valued velocity and acceleration/force boosts in Clifford Phase Spaces and find an explicit Clifford algebraic realization of the velocity and acceleration/force boosts. Finally, we provid...

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law “angle of incidence equals angle of reflection” are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. This is a magnetic analog of Hilbert’s fourth problem asking to describe the Fin...