Advertisement

On the Riemann curvature of diffeomorphism groups

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

Abstract

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.

Keywords

Sectional Curvature Riemann Curvature Diffeomorphism Group Constant Negative Curvature Riemannian Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© French Acad. Sciences, Paris 1965

Authors and Affiliations

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

Personalised recommendations