Symmetries of Contact Metric Manifolds

Details Symmetries of Contact Metric Manifolds Symmetries of Contact Metric Manifolds

2002-03-09

arxiv.org/abs/math/0203090v2

Geometriae Dedicata 101 (2003), 203-216

Mathematics

Differential Geometry

14 pages, LaTeX2e, some comments and references added

Scientific paper

10.1023/A:1026375212252

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.

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