Aghasi, M and Bahari, AR and Dodson, CTJ and Galanis, GN and Suri, A (2008) Second order structures for sprays and connections on Fréchet manifolds. [MIMS Preprint]
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Abstract
Ambrose, Palais and Singer introduced the concept of second order structures on finite dimensional manifolds. Kumar and Viswanath extended these results to the category of Banach manifolds. In the present paper all of these results are generalized to a large class of Fréchet manifolds. It is proved that the existence of Christoffel and Hessian structures, connections, sprays and dissections are equivalent on those Fréchet manifolds which can be considered as projective limits of Banach manifolds. These concepts provide also an alternative way for the study of ordinary differential equations on non-Banach infinite dimensional manifolds. Concrete examples of the structures are provided using direct and flat connections.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | Banach manifold, Fréchet manifold, Hessian structure, Christoffel structure, connection, spray, dissection, geodesic, ordinary differential equations |
| 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: | 29 Oct 2008 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1161 |
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