Soma Maity

Let $M$ be a closed smooth manifold. Consider the Riemannian functional $\mathcal{R}_p$ defined by the $L^p$-norm of Riemannian curvature tensor. It is a real valued function defined on the space of unit volume Riemannian metrics on $M$. Compact irreducible symmetric spaces are critical metrics for every Riemannian functionals. I will talk about the stability and local minimizing properties of $\mathcal{R}_p$ at these metrics.