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Displaying similar documents to “Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds”

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...

Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

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Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection ∇ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the ∇ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of ∇ -parallel vector fields.

Metrization of connections with regular curvature

Alena Vanžurová (2009)

Archivum Mathematicum

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We discuss Riemannian metrics compatible with a linear connection that has regular curvature. Combining (mostly algebraic) methods and results of [4] and [5] we give an algorithm which allows to decide effectively existence of positive definite metrics compatible with a real analytic connection with regular curvature tensor on an analytic connected and simply connected manifold, and to construct the family of compatible metrics (determined up to a scalar multiple) in the affirmative...