Anusha Mangala Krishnan
Syracuse University, USA
February 25, 2021
Prescribing Ricci curvature on a product of spheres: The Ricci curvature Ric$(g)$ is a symmetric 2-tensor on a Riemannian manifold $(M,g)$ that encodes curvature information. The Ricci curvature features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation. The nature of Ric$(g)$ as a differential operator in particular its nonlinearity and the fact that it is degenerate make these PDEs particularly challenging. In this talk I will address the following question. Given a symmetric 2-tensor $T$ on a manifold $M$, does there exist a metric $g$ such that Ric$(g) = T$? I will discuss some classical results as well as some recent work in the presence of symmetry.
Syracuse University, USA
February 25, 2021
Prescribing Ricci curvature on a product of spheres: The Ricci curvature Ric$(g)$ is a symmetric 2-tensor on a Riemannian manifold $(M,g)$ that encodes curvature information. The Ricci curvature features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation. The nature of Ric$(g)$ as a differential operator in particular its nonlinearity and the fact that it is degenerate make these PDEs particularly challenging. In this talk I will address the following question. Given a symmetric 2-tensor $T$ on a manifold $M$, does there exist a metric $g$ such that Ric$(g) = T$? I will discuss some classical results as well as some recent work in the presence of symmetry.