A note on symmetric connections |
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| Institution: | 1. Consortium for Fundamental Physics, Physics Department, Lancaster University, Lancaster LA1 4YB, UK;2. Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland |
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| Abstract: | In this paper we analyze a reciprocal of the fundamental theorem of Riemannian geometry. We give a condition for a symmetric connection to be locally the Levi-Civita connection of a metric. We also construct a couple of natural examples of connections on the n-dimensional torus and investigate the global problem. |
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