On the Riemann curvature of diffeomorphism groups
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.
KeywordsSectional Curvature Riemann Curvature Diffeomorphism Group Constant Negative Curvature Riemannian Domain
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