The aim of the present paper is to establish a global investigation of conformal changes in Finsler geometry. Under this change, we obtain the relationships between some geometric objects associated to (M, L) and the corresponding objects associated to $(M, ˜L)$. We have found explicit global expressions relating the two associated Cartan connections ∇ and ˜∇, the two associated Berwald connections D and ˜D and the two associated Barthel connections Γ and ˜Γ. The relationships between the corresponding curvature tensors have been also found. The relations thus obtained lead in turn to several interesting results.
Among the results obtained, is a characterization of conformal changes, a characterization of homotheties, some conformal invariants and conformal -invariants. In addition, several useful identities have been found. Although our treatment is entirely global, the local expressions of the obtained results, when calculated, coincide with the existing classical local results. |
