Quaternionic Kahler manifolds of cohomogeneity one

Andrew Dancer; Andrew Swann

doi:10.1142/S0129167X99000215

Quaternionic Kahler manifolds of cohomogeneity one

^*Corresponding author for this work

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Abstract

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.

Original language	English
Journal	International Journal of Mathematics
Volume	10
Issue	5
Pages (from-to)	541-570
Number of pages	30
ISSN	0129-167X
DOIs	https://doi.org/10.1142/S0129167X99000215
Publication status	Published - 1 Jan 1999
Externally published	Yes

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AB - 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.

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Quaternionic Kahler manifolds of cohomogeneity one

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