|
|||||
|
|
|
|
|
|
|
|
|
On a constrained
variational problem and the spaces of horizontal paths
Zhong Ge |
|
Vol. 149 (1991), No. 1, 61–94
|
Abstract |
|
In this paper we study geometry associated to an isoholonomy variational problem on a fat bundle. We prove that the energy function satisfies the Palais-Smale condition on the space of horizontal paths. We blow up the singularity of the horizontal loop space. Then we study the closed geodesics. We relate the number of connected components of the space of loops with trivial holonomy to the topology of the fat bundle. |
Mathematical Subject Classification 2000
Primary: 58E10
|
Milestones
Received: 15 August 1989
Revised: 3 March 1990
Published: 1 May 1991
|
Authors |
| Zhong Ge | |
|
