arXiv subjects
Publications and source records attributed to Sorin V. Sabau.
We study the variational problem for $N$-parallel curves on a Finslerian surface by means of Exterior Differential Systems using Griffiths' method. We obtain the conditions when these curves are extremals of a length functional and write the explicit form of Euler-Lagrange equations for this type of variational problem.
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.
We study the topology of complete Finsler manifolds admitting convex functions
The present paper shows that for a given integer k greater than 2 it is possible to construct an at least k-differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finsler sphere as well.
Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel vector field W, respectively. Moreover, the local 1-parameter group of Finslerian local isometries of the Kropina space coincides with the local 1-parameter group Riemannian of local isometries on (M, h).
We characterize the differentiable points of the distance function from a closed subset $N$ of an arbitrary dimensional Finsler manifold in terms of the number of $N$-segments. In the case of a 2-dimensional Finsler manifold, we prove the structure theorem of the cut locus of a closed subset $N$, namely that it is a local tree, it is made of countably many rectifiable Jordan arcs except for the endpoints of the cut locus and that an intrinsic metric can be introduced in the cut locus and its intrinsic and induced topologies coincide. We should point out that these are new results even for Riemannian manifolds.
The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two model spaces of them: the Euclidean space and the odd-dimensional spheres.
An (I,J,K)-generalized Finsler structure on a 3-manifold is a generalization of a Finslerian structure, introduced in order to separate and clarify the local and global aspects in Finsler geometry making use of the Cartan's method of exterior differential systems. In this paper, we show that there is a close relation between (I,J,1)-generalized Finsler structures and a class of contact circles, namely the so-called Cartan structures. This correspondence allows us to determine the topology of 3-manifolds that admit (I, J, 1)-generalized Finsler structures and to single out classes of (I, J, 1)-generalized Finsler structures induced by standard Cartan structures.
We study the necessary and sufficient conditions for a Finsler surface with $(α,β)$-metrics to be with reversible geodesics.