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

Abstract

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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References in corpus (1)

• Finsleroid-regular space. Landsberg-to-Berwald implication

Cited by in corpus (2)

• On a rigidity condition for Berwald Spaces
• Some Rigidity Conditions on Berwald Structures