Geodesic flows on path spaces

DOI10.1007/BF02881883zbMath1025.58016OpenAlexW1543895892MaRDI QIDQ1609660

Yong Liu, Kai-Nan Xiang

Publication date: 15 August 2002

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02881883

zbMATH Keywords

Wiener measuregeodesic flowquasi-invariancepath spacesnegative Markov connection

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (1)

Quasi-invariant transformations on the path space over manifolds

Cites Work

• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• A class of vector fields on path spaces
• Existence and uniqueness of geodesics on path spaces
• Renormalized differential geometry on path space: Structural equation, curvature
• Towards a Riemannian geometry on the path space over a Riemannian manifold
• Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold

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