Metrization of connections with regular curvature. (English) Zbl 1212.53020

Vanžurová, A.

Arch. Math., Brno 45, No. 4, 325-333 (2009).

Summary: We discuss Riemannian metrics compatible with a linear connection that has regular curvature. Combining (mostly algebraic) methods and results of O. Kowalski [Math. Z. 125, 129–138 (1972; Zbl 0234.53024); Note Mat. 8, No. 1, 1–11 (1988; Zbl 0699.53038)], we give an algorithm which allows to decide effectively the 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 briefly touch related problems concerning geodesic mappings and projective structures.

MSC:

53B05	Linear and affine connections
53B20	Local Riemannian geometry

Keywords:

manifold; linear connection; metric; pseudo-Riemannian geometry

Citations:

Zbl 0234.53024; Zbl 0699.53038