There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces

Details There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces

2008-10-10

arxiv.org/abs/0810.1937v6

Mathematics

Differential Geometry

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Scientific paper

We show that there are not pure $\mathcal{C}^5$ regular y-global Landsberg surfaced. The proof is based on the averaged connection associated with the linear Chern's connection and the classification of irreducibles holonomies of torsion-free affine connections. The structure consists on exausting all the possible cases and showing that in dimension 2 Landsberg condition implies Berwald condition.

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