There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces
Differential Geometry
2010-09-23 v6 Metric Geometry
Abstract
We show that there are not pure 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.
Cite
@article{arxiv.0810.1937,
title = {There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces},
author = {Ricardo Gallego Torrome},
journal= {arXiv preprint arXiv:0810.1937},
year = {2010}
}
Comments
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