| publication name | A global theory of conformal Finsler geometry |
|---|---|
| Authors | Nabil L. Youssef; S. H. Abed; A. Soleiman |
| year | 2008 |
| keywords | Conformal change; Cartan connection; Berwald connection; Barthel connection; Nonlinear connection; Spray; Jacobi field; $pi$-tensor field; Klein-Grifone formalism; Pullback formalism. |
| journal | Tensor, N. S. |
| volume | 69 |
| issue | Not Available |
| pages | 155-178 |
| publisher | Not Available |
| Local/International | International |
| Paper Link | Not Available |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
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.