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Left invariant Finsler manifolds are generalized Berwald

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

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Abstract (2. Language): 
In this note we show that a Lie group endowed with a left invariant Finsler function is a generalized Berwald manifold. This observation makes it possible to construct a whole class of generalized Berwald manifolds, thus satisfying a request of Hashiguchi [6]: '.. .find much more interesting examples'. In particular, we show that the Randers Lie group constructed by Libing and Mo in an un¬published manuscript is in fact a proper gerenalized Berwald manifold. We also have a look at the more specific bi-invariant case, and review some essential results concerning bi-invariant Finsler functions with (at least partly) new and conceptual proofs.
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REFERENCES

References: 

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