Quaternionic Kähler Manifolds of Cohomogeneity One

Details Quaternionic Kähler Manifolds of Cohomogeneity One Quaternionic Kähler Manifolds of Cohomogeneity One

1998-08-21

arxiv.org/abs/math/9808097v2

Internat. J. Math. 10 (1999), 541--570

Mathematics

Differential Geometry

35 pages, LaTeX + AMS macros Extra hypothesis added to cohomogeneity two hyperK\"ahler classification. To appear in Internat.

Scientific paper

Classification results are given for (i) compact quaternionic K\"ahler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperK\"ahler 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 K\"ahler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.

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