**SMS scnews item created by Boris Lishak at Wed 9 Oct 2019 1235**

Type: Seminar

Distribution: World

**Calendar1: 14 Oct 2019 1200-1300**

**CalLoc1: Carslaw 375**

CalTitle1: Arroyo -- The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups

Auth: borisl@dora.maths.usyd.edu.au

### Geometry and Topology Seminar

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

### Romina Arroyo (Queensland)

October 14, 12:00-13:00 in Carslaw 375
Seminar schedule

Please join us for lunch after the talk.

**Abstract:**
One of the most important challenges of Riemannian geometry is to understand the Ricci curvature tensor. An open problem related with it is to find a Riemannian metric \(g\) and a real number \(c>0\) satisfying
\[
\operatorname{Ric} (g) = c T,
\]
for some fixed symmetric \((0, 2)\)-tensor field \(T\) on a manifold \(M,\) where \(\operatorname{Ric} (g)\) denotes the Ricci curvature of \(g\).

The aim of this talk is discuss this problem within the class of naturally reductive metrics when \(M\) is a compact simple Lie group.

This talk is based on work in progress with Artem Pulemotov (The University of Queensland).