Conjugate connections and differential equations on infinite dimensional manifolds

Aghasi, M. and Dodson, C.T.J. and Galanis, G.N. and Suri, A. (2008) Conjugate connections and differential equations on infinite dimensional manifolds. In: VIII International Colloquium on Differential Geometry, 7-11 July 2008, Santiago de Compostela, Spain. (In Press)

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Abstract

On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T^2M bijectively correspond to linear connections. In this paper we classify such structures for those Frechet manifolds which can be considered as projective limits of Banach manifolds. We investigate also the relation between ordinary differential equations on Frechet spaces and the linear connections on their trivial bundle; the methodology extends to solve differential equations on those Frechet manifolds which are obtained as projective limits of Banach manifolds. Such equations arise in theoretical physics. We indicate an extension of the Earle and Eells foliation theorem to the Frechet case.

Item Type: Conference or Workshop Item (Paper)
Additional Information: This version has an additional section outlining a possible generalization of the Earle and Eells foliation theorem to a wide class of Frechet manifolds.
Uncontrolled Keywords: Banach manifold, Frechet manifold, connection, conjugate, ordinary differential equation, foliations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User: Prof CTJ Dodson
Date Deposited: 26 Jun 2008
Last Modified: 20 Oct 2017 14:12
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1116

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