Quaternionic Kähler Manifolds of Cohomogeneity One
Abstract
Description
Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.
35 pages, LaTeX + AMS macros Extra hypothesis added to cohomogeneity two hyperKähler classification. To appear in Internat. J. Math
35 pages, LaTeX + AMS macros Extra hypothesis added to cohomogeneity two hyperKähler classification. To appear in Internat. J. Math