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

Aghasi, M and Dodson, CTJ and Galanis, GN and Suri, A (2005) Infinite dimensional second order differential equations via $T^2M$. [MIMS Preprint]

PDF t2de.pdf Download (187kB)

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:	MIMS Preprint
Uncontrolled Keywords:	Banach manifold, Frechet manifold, connection, second tangent bundle, vector bundle, section, differential equation
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:	16 Dec 2005
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/126

Available Versions of this Item

• Infinite dimensional second order differential equations via $T^2M$. (deposited 16 Dec 2005) [Currently Displayed]
  • Infinite dimensional second order differential equations via $T^2M$. (deposited 20 Sep 2007)

Actions (login required)

View Item