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Almost-Riemannian Structures on Banach Manifolds: The Morse Lemma and the Darboux Theorem

Published online by Cambridge University Press:  20 November 2018

A. J. Tromba
A. J. Tromba*
Affiliation:
University of California, Santa Cruz, California
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In this paper we introduce the notion of an almost Riemannian manifold. Briefly speaking, an almost-Riemannian structure on a Banach manifold is a generalization of the notion of a Riemannian structure on a Hilbert manifold, common examples would be manifolds of maps modelled on the Sobolev spaces Lkp. The successful use of weak Riemannian structures in hard problems has been given by Ebin [2] and Ebin and Marsden [10].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 640 - 652
Copyright
Copyright © Canadian Mathematical Society 1976

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