Abstract. In this paper we study the local and global properties of a complete Hilbert manifold, proving results of finite dimensional Riemannian geometry in the context of Hilbert manifolds.

AMS Subject Classification (1991): 58B20, 53C21

Keyword(s): Riemannian geometry, Hilbert manifold, exponential map, sectional curvature

Received January 31, 2005, and in revised form September 23, 2005. (Registered under 5927/2009.)