Geometric properties near singular points of surfaces given by certain representation formulae

TL;DR

This paper analyzes the geometric characteristics of surfaces near singular points, focusing on curvature calculations and fold singularities, to deepen understanding of their local geometric behavior.

Contribution

It provides explicit calculations of singular and limiting normal curvatures for surfaces with specific representation formulae and studies fold singularities of smooth maps.

Findings

Calculated singular curvature and limiting normal curvature along singular points.

Analyzed fold singular points of smooth maps.

Enhanced understanding of local geometric properties near singularities.

Abstract

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points of the first kind. Moreover, we study fold singular points of smooth maps.