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A note on symmetric connections

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
56
Issue
3
Identifiers
DOI: 10.1016/j.geomphys.2005.01.010
Keywords
  • Connections
  • Metrics
  • Manifolds
  • Fundamental Theorem Of Riemannian Geometry
Disciplines
  • Mathematics

Abstract

Abstract In this paper we analyze a reciprocal of the fundamental theorem of Riemannian geometry. We give a condition for a symmetric connection to be locally the Levi-Civita connection of a metric. We also construct a couple of natural examples of connections on the n-dimensional torus and investigate the global problem.

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