Seminář Jednoty českých matematiků a fyziků se koná 25.11.2019 od 14.00 v posluchárně M5.

RNDr. Magdalena Hykšová, Ph.D. (Fakulta dopravní ČVUT Praha)

Teorie her: od salónních her k počítačovým sítím

Seminář z diferenciální geometrie pokračuje 18.11.2019 od 10:00 v učebně M5

Hanci Chi (McMaster University/UHK University):

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

Abstrakt:
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.