Symplectic geometry of the loop space of a Riemannian manifold

DOI10.1016/0393-0440(94)00033-ZzbMath0826.58006WikidataQ115363107 ScholiaQ115363107MaRDI QIDQ1894597

Tilmann Wurzbacher

Publication date: 3 August 1995

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

diffeomorphism action on loopsinfinite dimensional symplectic geometry

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Group actions and symmetry properties (58D19)

Related Items

GEOMETRIC STRUCTURES ON PATH SPACES ⋮ A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold ⋮ Twistor spaces and spinors over loop spaces ⋮ WEIGHTED TRACES ON ALGEBRAS OF PSEUDO-DIFFERENTIAL OPERATORS AND GEOMETRY ON LOOP GROUPS ⋮ Geometric structures on loop and path spaces ⋮ The geodesic flow on a Riemannian supermanifold ⋮ The 2-Hilbert space of a prequantum bundle gerbe ⋮ Geodesics on path spaces and double category ⋮ Chern forms on mapping spaces

Cites Work

• The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group
• Coadjoint orbits of the Virasoro group
• Stratified symplectic spaces and reduction
• Geometry of manifolds of maps
• Iterated integrals of differential forms and loop space homology
• The inverse function theorem of Nash and Moser
• Riemannian geometry
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