Positivity for the curvature of the diffeomorphism group corresponding to the incompressible Euler equation with Coriolis force | Zendy

Taito Tauchi | Zendy; Tsuyoshi Yoneda | Zendy

Open Access

Positivity for the curvature of the diffeomorphism group corresponding to the incompressible Euler equation with Coriolis force

Author(s) -

Taito Tauchi,

Tsuyoshi Yoneda

Publication year - 2021

Publication title -

progress of theoretical and experimental physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.887

H-Index - 53

ISSN - 2050-3911

DOI - 10.1093/ptep/ptab043

Subject(s) - physics , diffeomorphism , curvature , geodesic , group (periodic table) , euler equations , sectional curvature , mathematical physics , conjugate points , compressibility , euler angles , euler's formula , mathematical analysis , scalar curvature , geometry , mathematics , quantum mechanics , mechanics

We investigate the geometry of the central extension $\widehat{\mathcal D}_{\mu}(S^{2})$ of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with an $L^{2}$-metric, for which geodesics correspond to solutions of the incompressible Euler equation with Coriolis force. In particular, we calculate the Misiołek 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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research