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A global theory of conformal Finsler geometry

Tensor, N. S. • 2008
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Publication Information
Authors Nabil L. Youssef; S. H. Abed; A. Soleiman
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.
Publisher Not Available
Volume 69
Issue Not Available
Pages 155-178
publication.type International
Paper Link Not Available
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.