For Frechet manifolds by using sprays, we construct connection maps, linear symmetric connections on tangent and second-order tangent bundles. We characterize linear symmetric connections on tangent bundles by using the bilinear symmetric mappings associated with a given spray on a manifold. Moreover, we give another characterization of linear symmetric connections on tangent bundles using tangent structures. We prove that there is a bijective correspondence between linear symmetric connections on tangent bundles and connection maps induced by sprays on a manifold.PDF: Geometry Via Sprays on Frechet Manifolds.pdf
