Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit

Details Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit

2009-08-27

arxiv.org/abs/0908.3965v1

Journal of Geometry and Physics 60 (2010) 1069 - 1088

Mathematics

Differential Geometry

37 pages, no figures

Scientific paper

10.1016/j.geomphys.2010.03.006

We classify all cohomogeneity one manifolds with principal orbit Q^111=SU(2)^3/U(1)^2 or M^110=(SU(3) x SU(2))/(SU(2) x U(1)) whose holonomy is contained in Spin(7). Various metrics with different kinds of singular orbits can be constructed by our methods. It turns out that the holonomy of our metrics is automatically SU(4) and that they are asymptotically conical. Moreover, we investigate the smoothness of the metrics at the singular orbit.

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