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On characterization of Poisson and Jacobi structures

Janusz Grabowski, Paweŀ Urbański (2003)

Open Mathematics

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.

On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Csaba Vincze, Tahere Reza Khoshdani, Sareh Mehdi Zadeh Gilani, Márk Oláh (2019)

Communications in Mathematics

In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.

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