Acceleration bundles on Banach and Fréchet manifolds

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 (Unpublished)

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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

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