Bundles of acceleration on Banach manifolds

Dodson, CTJ and Galanis, GN (2005) Bundles of acceleration on Banach manifolds. Nonlinear Analysis, 63 (5-7). pp. 465-471. ISSN 0362-546X

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Abstract

We consider an infinite dimensional manifold M modelled on a Banach space E and we construct smooth fiber bundle structures on the tangent bundle of order two T^2M, which consists of all smooth curves of M that agree up to their acceleration, as well as on the corresponding second order frame bundle L^2M. These bundles prove to be associated with respect to the identity representation of the general linear group GL(E}) that serves as the structure group of both of them. Moreover, a bijective correspondence between linear connections on T^2M and connection forms of L^2M is revealed.

Item Type:	Article
Uncontrolled Keywords:	Banach manifold, second tangent bundle, second frame bundle, connection, acceleration bundle
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:	13 Dec 2005
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/122

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