Some positivity results of the curvature on the group corresponding to the incompressible Euler equation with Coriolis force

2021/02/27 by Taito Tauchi, Tauchi, Taito, Tsuyoshi Yoneda +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics (physics.geo-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2103.00192

openalex publication_date 2021/02/27 · openalex created_date 2021/03/15 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate the geometry of a central extension \widehat\mathcal D_μ(S²) of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with the L²-metric, whose geodesics correspond solutions of the incompressible Euler equation with Coriolis force. In particular, we calculate the Misiolek curvature of this group. This value is related to the existence of a conjugate point and its positivity directly implies the positivity of the sectional curvature.

Cited by

• Conjugate and cut points in ideal fluid motion

Related

• Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoid
• Arnold stability and Misiołek curvature
• Almost positive curvature on the Gromoll-Meyer sphere
• Curvatures of Sobolev metrics on diffeomorphism groups
• Bi-invariant metric on contact diffeomorphisms group