Andrei Moroianu

Andrei Moroianu works in differential geometry, including Kähler geometry and geometric differential operators. His authored lectures develop the interaction of a Riemannian metric, a complex structure $J$, and the associated Kähler form $\omega (X,Y)=g(JX,Y)$. For a Kähler manifold, the Levi-Civita connection preserves $J$, linking the real and complex descriptions of curvature.^[ref]

A concrete consequence is that the Ricci form represents the tangent First Chern class; prescribing Ricci curvature therefore has a topological constraint, not just a differential equation. His lectures explain the Kähler-Einstein metric equation and illustrate it on Complex projective space and Ricci-flat examples.^[ref] His personal page identifies him as a CNRS research director.^[ref]