English

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 C5\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.

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

This paper has been withdrawn by the author

R2 v1 2026-06-21T11:29:35.257Z