Frame bundle of Riemannian path space and Ricci tensor in adapted differential geometry

DOI10.1006/jfan.2000.3634zbMath1010.58026OpenAlexW2031858415MaRDI QIDQ1589676

Paul Malliavin, Ana Bela Cruzeiro

Publication date: 12 December 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.2000.3634

zbMATH Keywords

Ricci tensorWeitzenböck formulaMarkovian connectionframe bundleRiemannian path space

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (7)

Tangent processes on Wiener space ⋮ Itô maps and analysis on path spaces ⋮ Finite dimensional approximation of Riemannian path space geometry. ⋮ Markovian connection, curvature and Weitzenböck formula on Riemannian path spaces ⋮ Horizontal lift of Ornstein-Uhlenbeck process over Riemannian path space ⋮ Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry ⋮ Stochastic calculus of variations and Harnack inequality on Riemannian path spaces

Cites Work

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• The Ornstein-Uhlenbeck process over the space of Riemannian paths and the martingale problem
• De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
• Stochastic calculus with anticipating integrands
• Formules de la moyenne, calcul de perturbations et théoremes d'annulation pour les formes harmoniques
• Renormalized differential geometry on path space: Structural equation, curvature
• Twisted sheets

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