On Berwald and Wagner manifolds.
On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach
In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.
On -complex Finsler spaces.
On Finsler connections.
A new definition for lifts and lowerings is given, linking the different tensor algebras involved in the usual treatment of Finsler manifolds. By means of them, the relation between the different classes of linear connections is made clearer.
On Finslerian hypersurfaces given by -changes.
On generalized Douglas-Weyl Randers metrics
We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is...
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
On isotropic Berwald metrics
We prove that every isotropic Berwald metric of scalar flag curvature is a Randers metric. We study the relation between an isotropic Berwald metric and a Randers metric which are pointwise projectively related. We show that on constant isotropic Berwald manifolds the notions of R-quadratic and stretch metrics are equivalent. Then we prove that every complete generalized Landsberg manifold with isotropic Berwald curvature reduces to a Berwald manifold. Finally, we study C-conformal changes of isotropic...
On -Hamilton geometry.
On nonlinear connections in higher order Lagrange spaces.
On projectable objects on fibred manifolds
The aim of this paper is to study the projectable and -projectable objects (tensors, derivations and linear connections) on the total space of a fibred manifold , where is a normalization of .
On special hypersurface of a Finsler space with the metric .
On the Chern-Weil homomorphism in Finsler spaces.
On the Finsler geometry of the Heisenberg group and its extension
We first classify left invariant Douglas -metrics on the Heisenberg group of dimension and its extension i.e., oscillator group. Then we explicitly give the flag curvature formulas and geodesic vectors for these spaces, when equipped with these metrics. We also explicitly obtain -curvature formulas of left invariant Randers metrics of Douglas type on these spaces and obtain a comparison on geometry of these spaces, when equipped with left invariant Douglas -metrics. More exactly, we show...
On the geometries of superior order.
On the geometry of some para-hypercomplex Lie groups
In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...
On the homogeneous geometrical model of a Riemannian space.
On the projective Finsler metrizability and the integrability of Rapcsák equation
A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences...
On the Randers spaces of second order.
On the rheonomic Finslerian mechanical systems.