Let $M$ be a closed smooth manifold. Consider the space of Riemannian metrics $\\mathcal{M}$ on $M$. A real valued function on $\\mathcal{M}$ is called a Riemannian functional if it remains invariant under the action of the group of diffeomorphisms of $M$ on $\\mathcal{M}$. We will discuss some geometric properties of the critical points of certain natural Riemannian functionals in this lecture.

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Last updated: 18 May 2024