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2005.46: Infinite dimensional second order differential equations via $T^2M$

2005.46: M Aghasi, CTJ Dodson, GN Galanis and A Suri (2007) Infinite dimensional second order differential equations via $T^2M$. Nonlinear Analysis, 67. pp. 2829-2838. ISSN 0362-546X

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Abstract

The vector bundle structure obtained on the second order (acceleration) tangent bundle T^2M of a smooth manifold M by means of a linear connection on the base provides an alternative way for the study of second order differential equations on manifolds of finite and infinite dimension. Second order vector fields and their integral curves provide a new way of solving a wide class of second order differential equations on Frechet manifolds and may be used also to describe geodesic curves on a Riemannian manifold. The new technique proposed is illustrated by concrete examples within the framework of Banach and Frechet spaces as well as on Lie groups.

Item Type:Article
Uncontrolled Keywords:Banach manifold, Frechet manifold, connection, second tangent bundle, vector bundle, section, differential equation
Subjects:MSC 2000 > 53 Differential geometry
MSC 2000 > 58 Global analysis, analysis on manifolds
MIMS number:2005.46
Deposited By:Prof CTJ Dodson
Deposited On:20 September 2007

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