FIBRE BUNDLE MAPS AND COMPLETE SPRAYS IN FINSLERIAN SETTING

Mircea Crasmareanu
2009 Journal of the Korean Mathematical Society  
A theorem of Robert Blumenthal is used here in order to obtain a sufficient condition for a function between two Finsler manifolds to be a fibre bundle map. Our study is connected with two possible constructions: 1) a Finslerian generalization of usually Kaluza-Klein theories which use Riemannian metrics, the well-known particular case of Finsler metrics, 2) a Finslerian version of reduction process from geometric mechanics. Due to a condition in the Blumenthal's result the completeness of
more » ... ompleteness of Euler-Lagrange vector fields of Finslerian type is discussed in detail and two situations yielding completeness are given: one concerning the energy and a second related to Finslerian fundamental function. The connection of our last framework, namely a regular Lagrangian having the energy as a proper (in topological sense) function, with the celebrated Poincaré Recurrence Theorem is pointed out.
doi:10.4134/jkms.2009.46.3.551 fatcat:jepyyv722rdx5gegjikdfbplum