A note on quaternionic K\"ahler manifolds with ends of finite volume

TL;DR

This paper demonstrates the existence of complete, non-locally symmetric quaternionic Kähler manifolds with finite volume ends across all dimensions divisible by four, expanding the known examples in differential geometry.

Contribution

It proves the existence of such manifolds in all relevant dimensions, providing new examples in the study of quaternionic Kähler geometry.

Findings

Existence of non-locally symmetric quaternionic Kähler manifolds with finite volume ends in all dimensions 4m≥4.

Construction of examples in each dimension, broadening the class of known manifolds.

Advancement in understanding the geometric structure of quaternionic Kähler manifolds.

Abstract

We prove that complete non-locally symmetric quaternionic K\"ahler manifolds with an end of finite volume exist in all dimensions $4m\ge 4$.