We explain our recent study on the complex analytic structure of a small tubular neighborhood of a complex submanifold, which is based on T. Ueda's classification theory. We also explain how to apply them to: 

(i) a study on (non-) existence of a smooth Hermitian metric on a nef line bundle over a projective manifold with semi-positive curvature, and 

(ii) a study on non-projective and non-Kummer K3 surfaces.