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Metrics compatible with a symmetric connection in dimension three

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Publication Date
Volume
19
Issue
1
Identifiers
DOI: 10.1016/0393-0440(95)00014-3
Keywords
  • Riemannian Geometry
  • Metric
  • Connection
  • Curvature
Disciplines
  • Mathematics

Abstract

Abstract The problem of characterizing symmetric connections that are Levi-Civita connections of a pseudo-Riemannian metric is considered. A more or less complete solution of the problem in three dimensions is presented. In particular the single class of Levi-Civita connections whose metric is not determined up to a conformal factor by the curvature tensor alone is characterized in geometric terms.

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