There are no C⁵-Regular Pure y-Global Landsberg Surfaces

2008/10/10 by Ricardo Gallego Torromé, Ricardo Gallego Torrome, Torrome, Ricardo Gallego
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.0810.1937

This paper has been withdrawn by the author

openalex publication_date 2008/10/10 · arxiv created 2010/09/22 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there are not pure C⁵ 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.

Citations

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

Cited by

• On a rigIDity condition for Berwald spaces

Related

• A note on L. Zhou's result on Finsler surfaces with K = 0 and J = 0
• On the existence of Generalized Unicorns on Surfaces
• The Finsler surface with K=0 and J=0
• A simply connected surface of general type with p_g=0 and K²=4
• Solutions for the Landsberg unicorn problem in Finsler geometry