Connections of Berwald type (Q2714308)

The paper is concerned with connections in some vector bundle over the tangent bundle \(\tau:TM\to M\) of a manifold \(M\). The main purpose is the construction of connections of Finsler geometry e.g. the Berwald connection, the Chern-Rund connection and others. The author shows that the most appropriate setting is the pull-back bundle \(\tau^*(TM)\) of the tangent bundle. The main result is that, given a horizontal distribution on \(TM\), there exists a certain linear connection on \(\tau^*(TM)\), which is uniquely defined by some geometric qualities. The construction does not make use of a Finsler metric. The vanishing of certain tensorial invariants resembling the classical torsion tensor of a linear connection on \(TM\) characterizes special connections as those mentioned above.