Symmetries of Contact Metric Manifolds

Abstract

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K--contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automorphism of the structure if and only if the manifold is obtained from the Konishi bundle of a compact pseudo--Riemannian quaternion--Kaehler manifold after changing the sign of the metric on a maximal negative distribution. We also prove that non--regular Sasakian manifolds are not homogeneous and construct examples with cohomogeneity one. Using these results we obtain in the last section the classification of all homogeneous Sasakian manifolds.

14 pages, LaTeX2e, some comments and references added

Cited by in corpus (6)

• On formality of Sasakian manifolds
• Killing vector fields of constant length on compact homogeneous Riemannian manifolds
• On simply connected K-contact non-Sasakian manifolds
• Killing vector fields of constant length on Riemannian manifolds
• A special class of holomorphic mappings and the Faddeev-Hopf model
• On compatible linear connections with totally anti-symmetric torsion tensor of three-dimensional generalized Berwald manifolds