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

TL;DR

This paper establishes a general existence theorem for local moduli spaces of geometric structures on manifolds and demonstrates its application to Sasakian and Sasaki-Einstein structures.

Contribution

It introduces a broad existence theorem for local moduli spaces and applies it specifically to Sasakian and Sasaki-Einstein structures.

Findings

Proved a general local moduli space existence theorem.

Applied the theorem to Sasakian and Sasaki-Einstein structures.

Enhanced understanding of geometric structures on manifolds.

Abstract

In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.