On the Riemann curvature of diffeomorphism groups

  • Vladimir I. Arnold
Part of the Vladimir I. Arnold - Collected Works book series (ARNOLD, volume 2)


One calculates explicitly the sectional curvatures of certain infinite-dimensional Lie groups equipped with left-invariant metrics whose geodesics correspond to flows of an ideal fluid. The sectional curvature turns out to be negative in certain two-dimensional directions.


Sectional Curvature Riemann Curvature Diffeomorphism Group Constant Negative Curvature Riemannian Domain 
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Copyright information

© French Acad. Sciences, Paris 1965

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.HeidelbergGermany

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