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Totally geodesic subgroups of diffeomorphisms |
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| Authors: | Stefan Haller Josef Teichmann Cornelia Vizman |
| Institution: | a Institute of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090, Vienna, Austria b Institute of Financial and Actuarial Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria c Department of Mathematics, West University of Timisoara, Bd. V. Parvan 4, 1900, Timisoara, Romania |
| Abstract: | We determine the Riemannian manifolds for which the group of exact volume preserving diffeomorphisms is a totally geodesic subgroup of the group of volume preserving diffeomorphisms, considering right invariant L2-metrics. The same is done for the subgroup of Hamiltonian diffeomorphisms as a subgroup of the group of symplectic diffeomorphisms in the Kähler case. These are special cases of totally geodesic subgroups of diffeomorphisms with Lie algebras big enough to detect the vanishing of a symmetric 2-tensor field. |
| Keywords: | Groups of diffeomorphisms as manifolds Geodesic equations on infinite dimensional Lie groups |
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