Cartan and Berwald connections in the pullback formalism

Details Cartan and Berwald connections in the pullback formalism Cartan and Berwald connections in the pullback formalism

2007-07-09

arxiv.org/abs/0707.1320v2

Algebras, Groups and Geometries, 25, 4(2008), 363-386.

Mathematics

Differential Geometry

LaTeX file, 14 pages, fundamental changes of the paper

Scientific paper

Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, is introduced and investigated. Moreover, it is shown that for the Cartan and Berwald connections, the associated semispray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. An explicit intrinsic expression relating both connections is deduced.

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