Isospectral Metrics on Projective Spaces

We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In chapter 3 we will recall some facts about complex projective space. In chapter 4 we build the isospectral metrics. Chapter 5 is devoted to the non isometry proof of the metrics built in chapter 4. In chapter 6 isospectral metrics on real projective space are derived from metrics on the sphere.