Metrizability of connections on two-manifolds
Alena Vanžurová, Petra Žáčková (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the...