An Introduction to Harmonic Manifolds and the Lichnerowicz Conjecture

Abstract

The title is self-explanatory. We aim to give an easy to read and self-contained introduction to the field of harmonic manifolds. Only basic knowledge of Riemannian geometry is required. After we gave the definition of harmonicity and derived some properties, we concentrate on Z. I. Szab\'o's proof of Lichnerowicz's conjecture in the class of compact simply connected manifolds.