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 |
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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: | http://eprints.maths.manchester.ac.uk/id/eprint/122 |

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