Geometry of Bounded Frechet Manifolds

Abstract

In this paper we develop the geometry of bounded Fréchet manifolds. We prove that a bounded Fréchet tangent bundle admits a vector bundle structure. But the second order tangent bundle $T^{2}M$ of a bounded Fréchet manifold $M$, becomes a vector bundle over $M$ if and only if $M$ is endowed with a linear connection. As an application, we prove the existence and uniqueness of the integral curve of a vector field on $M$.

In this version we correct some gaps in the printed version

References in corpus (2)

• Second order tangent bundles of infinite dimensional manifolds
• Sard's theorem for mappings between Fréchet manifolds

Cited by in corpus (3)

• On the generalization of the Darboux theorem
• Finslerian geodesics on Fréchet manifolds
• A simple proof of the short-time existence and uniqueness for Ricci flow