Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry

DOI10.1006/jfan.2001.3765zbMath1011.60034OpenAlexW1974473290MaRDI QIDQ5952331

Ana Bela Cruzeiro, Shizan Fang

Publication date: 2 June 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2001.3765

zbMATH Keywords

Wiener measureRicci curvaturepath spaceWeitzenböck formulaMarkovian connection

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (5)

Integrability on direct limits of Banach manifolds ⋮ The vanishing of \(L^2\) harmonic one-forms on based path spaces ⋮ Finite dimensional approximation of Riemannian path space geometry. ⋮ An \(L^{2}\) theory for differential forms on path spaces. I ⋮ Horizontal lift of Ornstein-Uhlenbeck process over Riemannian path space

Cites Work

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• Quelques propriétés de l’intégrale stochastique du type noncausal
• An \(L^ 2\) estimate for Riemannian anticipative stochastic integrals

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