Examples of rigid and flexible Seifert fibred cone-manifolds

TL;DR

This paper presents examples of both rigid and flexible Seifert fibred cone-manifolds, illustrating the diversity within this class of geometric structures.

Contribution

It provides the first known examples of flexible Seifert fibred cone-manifolds alongside rigid ones.

Findings

Identified a rigid spherical Seifert fibred cone-manifold.

Constructed an example of a flexible Seifert fibred cone-manifold.

Demonstrated the coexistence of rigidity and flexibility in Seifert fibred structures.

Abstract

The present paper gives an example of a rigid spherical cone-manifold and that of a flexible one which are both Seifert fibred.