On the extendability of parallel sections of linear connections

2014/05/29 by Antonio J. Di Scala, Di Scala, Antonio J., Gianni Manno +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1405.7688

arxiv created 2014/05/29 · openalex publication_date 2014/05/29 · arxiv updated 2014/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π:E→ M be a vector bundle over a simply connected manifold and ∇ a linear connection in π. Let σ: U → E be a ∇-parallel section of π defined on a connected open subset U of M. We give sufficient conditions on U in order to extend σ to the whole M. We mainly concentrate to the case when M is a 2-dimensional simply connected manifold.

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