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We investigate the geometry of the central extension D̂µ(S2) of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with an L2-metric, for which geodesics correspond to solutions of the… Click to show full abstract
We investigate the geometry of the central extension D̂µ(S2) of the group of volume-preserving diffeomorphisms of the 2-sphere equipped with an L2-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.
Keywords:
incompressible euler;
euler equation;
positivity;
coriolis force;
group;
equation coriolis
Journal Title: Progress of Theoretical and Experimental Physics
Year Published: 2021
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Journal Title: Progress of Theoretical and Experimental Physics
Year Published: 2021
Link to full text (if available)
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recommendations!