Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two

TL;DR

This paper investigates the structure of noncompact Alexandrov spaces with nonnegative curvature and a codimension-two soul, showing that the Sharafutdinov retraction acts as a submetry under certain conditions.

Contribution

It provides new structural insights into Alexandrov spaces with codimension-two souls and proves the Sharafutdinov retraction is a submetry in this setting.

Findings

Sharafutdinov retraction is a submetry

Structural properties of Alexandrov spaces with codimension-two souls

Additional regularity assumptions lead to new geometric insights

Abstract

In this paper, we study a complete noncompact nonnegatively curved Alexandrov space $A$ with a soul $S$ of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, $\pi:\ A\to S$, is a submetry.