Affine Osserman connections and their Riemann extensions


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

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, cilt.11, ss.145-153, 1999 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 11 Konu: 2
  • Basım Tarihi: 1999
  • Doi Numarası: 10.1016/s0926-2245(99)00029-7
  • Dergi Adı: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
  • Sayfa Sayıları: ss.145-153

Özet

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.