A global theory of conformal Finsler geometry
Tensor, N. S. • 2008
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.
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.
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