Averaged Structures Associated with a Finsler Structure

Details Averaged Structures Associated with a Finsler Structure Averaged Structures Associated with a Finsler Structure

2005-01-05

arxiv.org/abs/math/0501058v9

Mathematics

Differential Geometry

changes in the introduction and in sections 4.3, 4.4, 4.5. Las sections deleted

Scientific paper

Given a Finsler structure ({\bf M},F) on a manifold {\bf M}, a Riemannian structure ({\bf M},h) and an affine connection \tilde{\nabla} on {\bf M} are defined. They are obtained as the {\it averaged} of the Finsler structure g and a specified linear connection in the bundle \pi^* {\bf TM} respectively. Parallel transport and curvatures of the averaged connection are obtained as well as a new local isometric invariant of the Finlser structure.

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