Zoll Manifolds of Type ${\mathbb{CP}}^n$ with Entire Grauert Tubes

Abstract

We show that a Zoll manifold of type ${\mathbb{CP}}^n$ with an entire Grauert tube is isometric to ${\mathbb{CP}}^n$ with the canonical Fubini-Study metric, up to constant multiplication.

19 pages, published version, comments very welcome