Curvatures of the diffeomorphism group and the space of volume elements

DOI10.1007/BF00971132zbMath0788.53036MaRDI QIDQ1204750

Nicolai Konstantinovich Smolentsev

Publication date: 28 March 1993

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Riemannian submersionssectional curvatures

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Global Riemannian geometry, including pinching (53C20)

Related Items (2)

The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow ⋮ The geometry of barotropic flow

Cites Work

• Unnamed Item
• Biinvariant metric on the group of diffeomorphisms of a three-dimensional manifold
• Infinite dimensional Lie transformation groups
• A biinvariant metric on the group of symplectic diffeomorphisms and the equation \((\partial/\partial t)\Delta F = \{\Delta F,F\}\)
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid

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