JP Journal of Geometry and Topology
Volume 21, Issue 3, Pages 265 - 294
(August 2018) http://dx.doi.org/10.17654/GT021030265 |
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ON THE CURVATURE OF FINSLER MANIFOLD UNDER PROJECTIVE TRANSFORMATION
M. Mehdi, M. Cheaito and M. Slayman
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Abstract: Using the Grifone formalism of the connection Γ[8] and the notations of Frölicher-Nijenhuis [4], for a Finsler manifold we establish that there exists a tensor W invariant under the projective transformation and that the curvature R of the homogenous Grifone-Ehersmann connection can be written as if and only if the tensor W vanishes, where ω and π are semi-basic forms, J is the vertical endomorphism and C is the Liouville vector field. |
Keywords and phrases: Finsler manifold, homogenous connection, spray, curvature, projective transformation. |
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