Tommy Murphy, McMaster University
“Rigidity results for Hermitian Einstein manifolds”
Motivated by work of A. Gray, we study a differential operator naturally defined on the unit sphere bundle of any Riemannian manifold (M,g). The coefficients of this differential operator are determined by the sectional curvatures of (M,g). This enabled Gray to prove rigidity results characterising the Hermitian symmetric spaces amongst Kaehler-Einstein manifolds. We will extend the study of his operator to various classes of Hermitian-Einstein manifolds, focusing in particular on nearly Kaehler manifolds and on Hermitian-Einstein surfaces. This is joint with Stuart Hall.