Quaternionic K\"ahler Manifolds of Cohomogeneity One
Differential Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/9808097,
title = {Quaternionic K\"ahler Manifolds of Cohomogeneity One},
author = {Andrew Dancer and Andrew Swann},
journal= {arXiv preprint arXiv:math/9808097},
year = {2007}
}
Comments
35 pages, LaTeX + AMS macros Extra hypothesis added to cohomogeneity two hyperK\"ahler classification. To appear in Internat. J. Math