Criteria for codimension two singularities of surfaces and their applications

TL;DR

This paper establishes straightforward criteria for identifying codimension two singularities on surfaces and applies these criteria to specific cases like ruled surfaces and center maps in Euclidean space.

Contribution

It introduces simple, practical criteria for classifying codimension two surface singularities and demonstrates their application to ruled surfaces and center maps.

Findings

Criteria for codimension two singularities on surfaces.

Conditions for singularities in ruled surfaces.

Conditions for singularities in center maps of surfaces.

Abstract

We give simple criteria for the singularities appearing on surfaces codimension less than or equal to two. As applications, we give conditions for codimension two singularities that appear in ruled surfaces and center maps of surfaces in the Euclidean space.