Curvature collineations of a spray manifold induced by the Lie symmetries of the underlying spray are studied. The basic observation is that the Jacobi endomorphism and the Berwald curvature are invariant under these symmetries; this implies the invariance of the further curvature data. Our main technical tool is an appropriate Lie derivative operator along the tangent bundle projection. M.S.C....

We study the existence of a natural ‘linearisation’ process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anc...

A linear connection on a Finsler manifold is called compatible to the function if its parallel transports preserve Finslerian length of tangent vectors. Generalized Berwald manifolds are equipped with connection. In paper we present general and intrinsic method characterize connections dimension three. We prove that not unique then indicatrices must be Euclidean surfaces revolution. The surplus...

We use two non-Riemannian curvature tensors, the χ-curvature and mean Berwald to characterise a class of Finsler metrics admitting first integrals. This includes constant flag curvature.