Isomorphism classes for Banach vector bundle structures of second tangents

Dodson, CTJ and Galanis, GN and Vassiliou, E (2006) Isomorphism classes for Banach vector bundle structures of second tangents. [MIMS Preprint]

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Abstract

On a smooth Banach manifold M, the equivalence classes of curves that agree up to acceleration form the second order tangent bundle T^2M of M. This is a vector bundle in the presence of a linear connection on M and the corresponding local structure is heavily dependent on the choice of connection. In this paper we study the extent of this dependence and we prove that it is closely related to the notions of conjugate connections and second order differentials. In particular, the vector bundle structure on T^2M remains invariant under conjugate connections with respect to diffeomorphisms of M.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Banach manifold, connection, second tangent bundle, isomorphism class, conjugacy
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User:	Prof CTJ Dodson
Date Deposited:	23 Jan 2006
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/114

Available Versions of this Item

• Isomorphism classes for Banach vector bundle structures of second tangents. (deposited 23 Jan 2006) [Currently Displayed]
  • Isomorphism classes for Banach vector bundle structures of second tangents. (deposited 16 Dec 2005)
    • Isomorphism classes for Banach vector bundle structures of second tangents. (deposited 04 Jun 2007)

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