Non compact Euclidean cone 3-manifolds with cone angles less than 2pi

TL;DR

This paper investigates the structure of noncompact Euclidean cone 3-manifolds with cone angles less than 2pi, providing classifications for specific angle ranges and describing their structure outside compact sets.

Contribution

It offers a detailed description of noncompact Euclidean cone 3-manifolds with cone angles below 2pi and classifies those with angles less than 3pi/2 or all angles equal to 3pi/2.

Findings

Classification of manifolds with cone angles less than 3pi/2

Description of structure outside compact sets

Characterization of manifolds with all cone angles equal to 3pi/2

Abstract

We describe some properties of noncompact Euclidean cone manifolds with cone angles less than c less than 2pi and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corollary we classify those with cone angles less than 3pi/2 and those with all cone angles equal to 3pi/2.