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2017-09-26  04:03 hrs.

Quaternion-Sasakian manifolds and reduction

Owen Dearricott
University of California

An n-Sasakian manifold is a Riemannian manifold foliated by equidistant n-dimensional totally geodesic leaves such that the Riemann tensor is that of a curvature one space form on any triple of vector fi elds the include a fi eld everywhere tangent to the leaves of the foliation. Such manifolds are intimately connected to the parallel even Cliff ord orbifolds of Moroianu and Semmelmann.

We discuss an analogue of 3-Sasakian reduction in this setting. It turns out in this general setting actions amenable to reduction are somewhat sparse. However the Quaternion-Sasakian case (n=3) have a rich supply that include inhomogeneous examples, reduction in this case closely ties back in with the 3-Sasakian reduction of Boyer, Galicki and Mann.

We also touch on some examples of 7-Sasakian circle reduction.

Palapa Guillermo Torres -- Miércoles 13 de agosto de 2014, 12:00 horas

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