Riemannian curvature on the group of area-preserving diffeomorphisms (motions of fluid) of 2-sphere

DOI10.1016/S0167-2789(96)00192-3zbMath0890.53060WikidataQ115339604 ScholiaQ115339604MaRDI QIDQ2364971

Kyo Yoshida

Publication date: 29 January 1997

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

instabilityperturbationincompressible fluidRiemannian manifoldEuler equationsectional curvaturegeodesic equationRiemannian curvature tensor

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Geodesics in global differential geometry (53C22) Hydrodynamic stability (76E99) Incompressible inviscid fluids (76B99) Foundations of fluid mechanics (76A02)

Related Items (4)

Instability of planetary flows using Riemann curvature: a numerical study ⋮ Curvature and stability of quasi-geostrophic motion ⋮ Diffeomorphism groups of compact manifolds ⋮ Nonpositive curvature on the area-preserving diffeomorphism group

Cites Work

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• Curvature of groups of diffeomorphisms preserving the measure of the 2- sphere
• 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
• Structure of the curvature tensor of the group of measure-preserving diffeomorphisms of a compact two-dimensional manifold
• Geodesics and curvature of a group of diffeomorphisms and motion of an ideal fluid
• A Riemannian geometrical description for Lie-Poisson systems and its application to idealized magnetohydrodynamics

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