没有$\mathcal{C}^5$ -正则纯$y$ -全局Landsberg曲面
There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces
摘要：
我们证明了不存在纯的$\mathcal{C}^5$正则y-整体Landsberg曲面.证明是基于与线性陈氏联络相关的平均联络和无挠仿射联络的不可约完整性的分类。结构包括exausting所有可能的情况下，并表明在2维Landsberg条件意味着Berwald条件。
英文摘要：
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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