On the Chern-Weil homomorphism in Finsler spaces

Kovács, Zoltán (2001) On the Chern-Weil homomorphism in Finsler spaces. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 17 (2). pp. 131-135. ISSN 0866-0174

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Abstract

In this paper a framework is set up which enables the author to formulate the Chern-Weil homomorphism on a Finsler space over a manifold M. For this end the following theorem is proved: Let (∇,h) be the h-Finsler connection, f p an invariant polynomial in HM. If for the curvature R 2 of the Cartan connection ∇R 2 =0 holds, then d h f * p (R 2 ,⋯,R 2 )=0, i.e. f * p is a d h -closed 2p-form. For Landsberg spaces holds ∇R 2 =0. In the case of non-vanishing d h a natural way to define cohomology groups is discussed.

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