3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients

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dc.creatorBoyer, Charles P.
dc.creatorGalicki, Krzysztof
dc.creatorPiccinni, Paolo
dc.date2000-07-29
dc.date.accessioned2026-07-07T04:36:34Z
dc.date.available2026-07-07T04:36:34Z
dc.descriptionUsing 3-Sasakian reduction techniques we obtain infinite families of new 3-Sasakian manifolds $\scriptstyle{{\cal M}(p_1,p_2,p_3)}$ and $\scriptstyle{{\cal M}(p_1,p_2,p_3,p_4)}$ in dimension 11 and 15 respectively. The metric cone on $\scriptstyle{{\cal M}(p_1,p_2,p_3)}$ is a generalization of the Kronheimer hyperkähler metric on the regular maximal nilpotent orbit of $\scriptstyle{{\Got s}{\Got l}(3,\bbc)}$ whereas the cone on $\scriptstyle{{\cal M}(p_1,p_2,p_3,p_4)}$ generalizes the hyperkähler metric on the 16-dimensional orbit of $\scriptstyle{{\Got s}{\Got o}(6,\bbc)}$. These are first examples of 3-Sasakian metrics which are neither homogeneous nor toric. In addition we consider some further $\scriptstyle{U(1)}$-reductions of $\scriptstyle{{\cal M}(p_1,p_2,p_3)}$. These yield examples of non-toric 3-Sasakian orbifold metrics in dimensions 7. As a result we obtain explicit families $\scriptstyle{{\cal O}(Θ)}$ of compact self-dual positive scalar curvature Einstein metrics with orbifold singularities and with only one Killing vector field.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0007184
dc.identifierhttp://arxiv.org/abs/math/0007184
dc.identifierAnnals of Global Analysis and Geometry 21, 85-110, 2002.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59645
dc.subjectDifferential Geometry
dc.title3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients
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