Affine Osserman connections and their Riemann extensions

✍ Scribed by E. García-Río; D.N. Kupeli; M.E. Vázquez-Abal; R. Vázquez-Lorenzo

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 626 KB
• Volume: 11
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(99)00029-7

✦ Synopsis

Osserman property is studied for affine torsion-free connections with special attention to the 2dimensional 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.