Displaying similar documents to “Compatible flat metrics.”

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 2 -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...

Hierarchy of integrable geodesic flows.

Peter Topalov (2000)

Publicacions Matemàtiques

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A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.