Metrization of connections with regular curvature

Alena Vanžurová

Address: Department of Algebra and Geometry Faculty of Science, Palacký University Tomkova 40, 779 00 Olomouc, Czech Republic


Abstract: 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.

AMSclassification: primary 53B05; secondary 53B20.

Keywords: manifold, linear connection, metric, pseudo-Riemannian geometry.