Non-compact Einstein manifolds with unimodular isometry group

Christoph Böhm, Ramiro A. Lafuente

Published 2023-07-25Version 1

We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative Einstein manifold. The proof involves the theory of polar actions, Lie-theoretic arguments and maximum principles.