The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups

ARROYO, ROMINA M.; ZILLER, WOLFGANG; PULEMOTOV, ARTEM

Melbourne

Congreso; Annual meeting of the Australian Mathematical Society; 2019

An interesting open problem is to find a Riemannian metric whose Ricci curvature is prescribed, that is, a Riemannian metric g and a real number c > 0 satisfyingRic(g) = cT;for some fixed symmetric (0; 2)-tensor eld T on a manifold M; where Ric(g) denotes the Ricci curvature of g:The aim of this talk is to discuss this problem within the class of naturally reductive metrics when M is a compact simple Lie group, and present recently obtained results in this setting.This talk is based on work in progress with Artem Pulemotov (The University of Queensland) and Wolfgang Ziller (University of Pennsylvania).