Totally geodesic subgroups of diffeomorphisms

✍ Scribed by Stefan Haller; Josef Teichmann; Cornelia Vizman

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 111 KB
• Volume: 42
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00096-1

✦ Synopsis

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 L 2 -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.