Affine Osserman connections and their Riemann extensions

Garcia-Rio, E
Kupeli, DN
Vazquez-Abal, ME
Vazquez-Lorenzo, R
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.


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Citation Formats
E. Garcia-Rio, D. Kupeli, M. Vazquez-Abal, and R. Vazquez-Lorenzo, “Affine Osserman connections and their Riemann extensions,” DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, pp. 145–153, 1999, Accessed: 00, 2020. [Online]. Available: