Narrow Results

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 (with; being a concurrent π-vector field), is established. The relation between the two Barthel connections Γ and , corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection, and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded.

It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

The present paper deals with an intrinsic investigation of the notion of a parallel π-vector field on the pullback bundle of a Finsler manifold (M, L). The effect of the existence of a parallel π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (with being a parallel π-vector field), is established. The relation between the two Barthel connections Γ and , corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-change of the fundamental linear connection in Finsler geometry: The Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded.

It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

The present paper deals with an intrinsic generalization of the conformal change and energy β-change on a Finsler manifold (M.L.), namely the energy β-conformal change ( with ; being a concurrent π-vector field and σ(x) is a function on M). The relation between the two Barthel connections Γ and , corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-conformal change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is obtained.

It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.