A class of locally inhomogeneous complete quaternionic K\"ahler manifolds

TL;DR

This paper proves that one-loop deformations of quaternionic Kähler manifolds in the c-map class are locally inhomogeneous, revealing their symmetry properties and inhomogeneity structure.

Contribution

It establishes the inhomogeneity of one-loop deformations of c-map quaternionic Kähler manifolds and characterizes their isometry groups.

Findings

One-loop deformations are locally inhomogeneous.

Full isometry groups have cohomogeneity one.

Results apply to all c-map spaces.

Abstract

We prove that the one-loop deformation of any quaternionic K\"ahler manifold in the class of c-map spaces is locally inhomogeneous. As a corollary, we obtain that the full isometry group of the one-loop deformation of any homogeneous c-map space has precisely cohomogeneity one.