Differential Geometry and Topology

course: Toric self-dual Einstein metrics as quotients

speaker: Paolo Piccinni (Dipartimento di Matematica - Universita' Roma La Sapienza)

abstract: I will discuss some old and new self-dual Einstein metrics with two-dimensional isometry group. Compact examples with positive scalar curvature appear on orbifolds, and are obtained as quaternion Kaehler quotients by torus actions on quaternionic projective spaces. As such, they are related to the 7-dimensional 3-Sasakian manifolds discovered in 1. In negative scalar curvature, several complete smooth examples have been constructed. The approach I will present, exploited in 2, is again through quaternion Kaehler quotients. A classification will be given of metrics that can be obtained as quotients of the 8-dimensional quaternionic hyperbolic space HH2 and its indefinite signature analogue HH1,1 by one-dimensional group actions.

1 C.P. Boyer, K. Galicki, B. Mann, E.G. Rees: Compact 3-Sasakian 7-manifolds with arbitrary second Betti number, Invent. Math. 131 (1998), 321-344

2 C.P. Boyer, D. Calderbank, K. Galicki, P. Piccinni: Toric self-dual Einsten metrics as quotients (http:/it.arxiv.orgabsmath.DG0311145), to appear in Comm. Math. Physics

timetable:
Thu 14 Oct, 17:00 - 18:15, Sala Conferenze Centro De Giorgi
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