On the extendability of parallel sections of linear connections

Antonio J. Di Scala; Gianni Manno

On the extendability of parallel sections of linear connections

Differential Geometry 2014-05-30 v1

Authors: Antonio J. Di Scala , Gianni Manno

Abstract

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

Keywords

linear connection parallel section vector bundle extendability simply connected manifold covariant derivative

Cite

@article{arxiv.1405.7688,
  title  = {On the extendability of parallel sections of linear connections},
  author = {Antonio J. Di Scala and Gianni Manno},
  journal= {arXiv preprint arXiv:1405.7688},
  year   = {2014}
}

On the extendability of parallel sections of linear connections

Abstract

Keywords

Cite

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