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2005.40: Bundles of acceleration on Banach manifolds

2005.40: CTJ Dodson and GN Galanis (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 2000 > 53 Differential geometry
MSC 2000 > 58 Global analysis, analysis on manifolds
MIMS number:2005.40
Deposited By:Prof CTJ Dodson
Deposited On:13 December 2005

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