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Article

Vanžurová, Alena
Metrization of connections with regular curvature. (English). Archivum Mathematicum, vol. 45 (2009), issue 4, pp. 325-333
MSC: 53B05, 53B20, 53C05, 53C20 | MR 2591685 | Zbl 1212.53020
Keywords:
manifold; linear connection; metric; pseudo-Riemannian geometry
Summary:
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 case. We also breafly touch related problems concerning geodesic mappings and projective structures.
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