Talk:Hilbert manifold
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I don't think we can give an inner product structure to an arbitrary Hilbert manifold structure naturally. For the inner product structure, we need a compatibility between all the coordinate charts, just like in the case of a Riemannian manifold, we need some compatibilities between the charts to get a Riemannian structure. Vipul 17:37, 23 June 2007 (UTC)
On the references: the right book by Lang to be cited is "Fundamentals of Differential Geometry" and not "Introduction to Differentiable Manifolds". The latter only deals with finite dimensional manifolds. —Preceding unsigned comment added by 201.231.145.6 (talk) 05:03, 1 March 2011 (UTC)