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A nonlinear splitting on a fibre bundle is a generalization of an Ehresmannconnection. An example is given by the homogeneous nonlinear splitting of aFinsler function on the total manifold of a fibre bundle. We show howhomogeneous nonlinear splittings and nonlinear lifts can be used to constructsubmersions between Euclidean, Minkowski and Finsler spaces. As an applicationwe consider a semisimple Lie algebra and use our methods to give new examplesof Finsler functions on a reductive homogeneous space.

Homogeneous nonlinear splittings and Finsler submersions