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Jacobi fields in path space

Title
Jacobi fields in path space
Authors
Cho Y.S.Hong S.-T.
Ewha Authors
조용승홍순태
SCOPUS Author ID
조용승scopus; 홍순태scopus
Issue Date
2010
Journal Title
Journal of the Korean Physical Society
ISSN
0374-4884JCR Link
Citation
vol. 57, no. 6, pp. 1344 - 1349
Indexed
SCI; SCIE; SCOPUS; KCI WOS scopus
Abstract
We consider the path space of a curved manifold on which a point particle is introduced in a conservative physical system with constant total energy to formulate its action functional and geodesic equation with breaks on the path. The second variation of the action functional is exploited to yield the geodesic deviation equation and to discuss the Jacobi fields on the curved manifold. We investigate the topology of the path space by using the action functional on it and its physical meaning by defining the gradient of the action functional, the space of bounded flow energy solutions and the moduli space associated with the critical points of the action functional. We also consider the particle motion on the n-sphere Sn in a conservative physical system to discuss explicitly the moduli space of the path space, the corresponding homology groups and the Sturm-Liouville operators.
DOI
10.3938/jkps.57.1344
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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