arXiv subjects
Publications and source records attributed to Kyobeom Song.
We provide a partial answer to Burns' 1982 conjecture on the affineness of entire Grauert tubes: the complement of a codimension-one subset of an entire Grauert tube is affine. This result is obtained by establishing a generalized version of Demailly's criterion for affineness of Stein manifolds, which may be of independent interest.
We compute several algebraic indices of the algebraization of the tangent bundle of a Zoll manifold that admits an entire Grauert tube. As an application, we prove that any Zoll manifold of type $\mathbb{HP}^2$ with an entire Grauert tube is isometric to the canonical $\mathbb{HP}^2$.
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.