Deformations and Moduli of Structures on Manifolds: General Existence Theorem and Application to the Sasakian Case

Abstract

In this paper we deal with the moduli problem for geometric structures on manifolds. We prove an existence theorem of a local moduli space in a very general setting. Then, to show the strength of this result, we apply it to the case of Sasakian and Sasaki-Einstein structures for which until now only partial results were known.