Dodson, CTJ and Galanis, GA (2006) Acceleration bundles on Banach and Fréchet manifolds. In: JGP Editorial Board Scientific Meeting In Commemoration of Andre Lichnerowicz, 27- 29 June 2006, International School for Advanced Studies, Trieste, Italy. (Unpublished)
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Abstract
The second order tangent bundle T^2M of a smooth manifold M consists of the equivalence classes of curves on M that agree up to their acceleration. Dodson and Radivoiovici showed that in the case of a finite n-dimensional manifold M, T^2M becomes a vector bundle over M if and only if M is endowed with a linear connection. We have extended this result to M modeled on an arbitrary Banach space and more generally to those Fréchet manifolds which can be obtained as projective limits of Banach manifolds. Various structural properties have been deduced.
| Item Type: | Conference or Workshop Item (Paper) |
|---|---|
| Additional Information: | The pdf file is a slideshow of 34 slides. |
| Uncontrolled Keywords: | Banach manifold, Frechet manifold, connection, second order tangent 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: | 23 Jun 2006 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/311 |
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