Questions tagged [quaternionic-geometry]
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Quaternionic-Kahler metrics whose universal covers have only discrete isometry groups?
I am interested in quaternionic-Kahler metrics that are "as inhomogeneous as possible."
Every complete quaternionic-Kahler manifold $X$ I can remember hearing of is a discrete quotient of some $Y$, ...
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Are there topological obstructions to the existence of almost quaternionic structures on compact manifolds?
$\DeclareMathOperator\End{End}\newcommand\Id{\mathrm{Id}}\DeclareMathOperator\Sp{Sp}\DeclareMathOperator\SO{SO}$I start with some background, but people familiar with the subject may jump directly to ...
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The Hypercomplex Structure of $SU(3)$
(A) In this really stylish answer it is shown that one can define a family of complex structures $J_{\lambda}$ on the Lie group SU(3), dependent on the parameter $\lambda \in {\mathbb C}\backslash {\...
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Spin Structures for Quaternionic-Kaehler and Hyper-Kaehler Manifolds
As is well-known (see Friedrich's book for example) every Kähler manifold is spin (or at least spin$^c$) and the Dirac is given (up to a twist) by $\partial + \partial^*$. What happens in the ...
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Homogeneous Quaternionic-Kähler Structure of the Grassmannians?
Paraphrasing from Cortes' notes:
The quaternionic Kähler condition for a manifold $M$, means that $\operatorname{End}(T(M))$ admits a
parallel subbundle $Q$ which is locally spanned by $3$
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