Differential geometry seminar - November 18, 10am, lecture room M5 PDF Print

The seminar on differential geometry will continue with this lecture:

November 18, 10am, lecture room M5.

Hanci Chi (McMaster University/UHK University):

Invariant Einstein Metrics of Cohomogeneity One with Principal Orbits as Wallach Spaces


A Riemannian manifold (M, g) is Einstein if its Ricci tensor is a constant multiple of g. With its charm and influence in both mathematics and physics, the subject of Einstein metrics draws a great amount of attention from both communities. In this talk, we give an introduction to Einstein metrics of cohomogeneity one. Its construction reduces the Einstein equations to a system of ODEs. Then we introduce some new examples. They are vector bundles M whose principal orbit G/K are Wallach spaces. On each M, we found a 1-parameter continuous family of Ricci-flat metrics and a 2-parameter continuous family of negative Einstein metrics. In particular, the complete metric with G2 holonomy discovered by Robert Bryant and Simon Salamon is recovered in the construction.

Last Updated on Thursday, 14 November 2019 10:29