A rigidity theorem for quaternionic Kaehler structures

TL;DR

This paper investigates the moduli space of quaternionic Kähler structures on compact manifolds of dimension 4n, establishing a rigidity theorem for structures with nonzero scalar curvature through Riemannian geometric analysis.

Contribution

It provides a new rigidity theorem for quaternionic Kähler structures of nonzero scalar curvature using Riemannian geometry, independent of twistor theory.

Findings

Rigidity theorem for quaternionic Kähler structures with nonzero scalar curvature

Analysis of the moduli space of quaternionic Kähler structures

Application of Riemannian geometric methods to study these structures

Abstract

We study the moduli space of quaternionic Kaehler structures on a compact manifold of dimension 4n (n>2) from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kaehler structures of nonzero scalar curvature by observing the moduli space.