Geodesic
Metrization of connections with regular curvature
Archivum mathematicum, Tome 45 (2009) no. 4, pp. 325-333.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 53B05, 53B20, 53C05, 53C20
Keywords: manifold; linear connection; metric; pseudo-Riemannian geometry 
@article{ARM_2009__45_4_a7,
     author = {Van\v{z}urov\'a, Alena},
     title = {Metrization of connections with regular curvature},
     journal = {Archivum mathematicum},
     pages = {325--333},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
     mrnumber = {2591685},
     zbl = {1212.53020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a7/}
}
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Vanžurová, Alena. Metrization of connections with regular curvature. Archivum mathematicum, Tome 45 (2009) no. 4, pp. 325-333. http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a7/