Geometry Via Sprays on Frechet Manifolds

Abstract

We construct connection maps and linear symmetric connections on tangent and second-order tangent bundles for \fr manifolds using the notion of a spray. For these manifolds, we characterize linear symmetric connections on tangent bundles in terms of bilinear symmetric mappings associated with sprays. We also provide an alternative characterization of these connections using tangent structures. Furthermore, we prove that a bijective correspondence exists between linear symmetric connections on tangent bundles and sprays.