Deformations of Compact Complex Manifolds with Ample Canonical Bundles*

In this paper, the author discusses the deformations of compact complex manifolds with ample canonical bundles. It is known that a complex manifold has unobstructed deformations when it has a trivial canonical bundle or an ample anti-canonical bundle.When the complex manifold has an ample canonical bundle, the author can prove that this manifold also has unobstructed deformations under an extra condition.