Affine Osserman connections and their Riemann extensions


Garcia-Rio E., Kupeli D., Vazquez-Abal M., Vazquez-Lorenzo R.

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, vol.11, no.2, pp.145-153, 1999 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 1999
  • Doi Number: 10.1016/s0926-2245(99)00029-7
  • Journal Name: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.145-153
  • Keywords: Osserman space, affine connection, Riemann extensions, MANIFOLDS

Abstract

Osserman property is studied for affine torsion-free connections with special attention to the 2-dimensional case. As an application, examples of nonsymmetric and even not locally homogeneous Osserman pseudo-Riemannian metrics are constructed on the cotangent bundle of a manifold equipped with a torsionfree connection by looking at their Riemann extensions. Also, timelike and spacelike Osserman conditions are analyzed for general pseudo-Riemannian manifolds showing that they are equivalent.