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Nonpositive curvature on the area-preserving diffeomorphism group

✍ Scribed by Stephen C. Preston


Book ID
108137666
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
190 KB
Volume
53
Category
Article
ISSN
0393-0440

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Riemannian curvature on the group of are
✍ Kyo Yoshida πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 567 KB

Euler's equation for an incompressible fluid filled in a Riemannian manifold D is regarded as a geodesic equation on the group of volume-preserving diffeomorphisms of D provided with a one-sided invariant metric. A negative sectional curvature implies instability of the geodesic with respect to the