Displaying similar documents to “Lifts of generalized symmetric spaces to tangent bundles”

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...

Curvatures of the diagonal lift from an affine manifold to the linear frame bundle

Oldřich Kowalski, Masami Sekizawa (2012)

Open Mathematics

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We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.