Displaying similar documents to “Spaces with non-symmetric affine connection.”

On metrizability of locally homogeneous affine 2-dimensional manifolds

Alena Vanžurová (2013)

Archivum Mathematicum

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In [19] we proved a theorem which shows how to find, under particular assumptions guaranteeing metrizability (among others, recurrency of the curvature is necessary), all (at least local) pseudo-Riemannian metrics compatible with a given torsion-less linear connection without flat points on a two-dimensional affine manifold. The result has the form of an implication only; if there are flat points, or if curvature is not recurrent, we have no good answer in general, which can be also...

How many are affine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2014)

Archivum Mathematicum

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The question how many real analytic affine connections exist locally on a smooth manifold M of dimension n is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.