2007/06/01 by Yong Seung Cho, Cho, Yong Seung, Soon-Tae Hong +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0706.0057
6 pages
arxiv created 2007/06/01 · openalex publication_date 2007/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 together 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 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 the conservative physical system to discuss explicitly the moduli space of the path space and the corresponding homology groups.