On a constrained variational problem and the space of horizontal paths (Q582659)
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scientific article; zbMATH DE number 4131305
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a constrained variational problem and the space of horizontal paths |
scientific article; zbMATH DE number 4131305 |
Statements
On a constrained variational problem and the space of horizontal paths (English)
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1991
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We study the geometry in an isoholonomy variational problem on a fat bundle. We prove that the energy functional satisfies the Palais-Smale condition on the space of horizontal paths and 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.
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blowing-up
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isoholonomy variational problem
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Palais-Smale condition
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connected components
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