Boundedness of geometric invariants near a singularity which is a suspension of a singular curve

TL;DR

This paper investigates how geometric invariants behave near singular points of surfaces formed as suspensions of singular curves, focusing on their boundedness and divergence orders.

Contribution

It provides a detailed analysis of the boundedness and divergence orders of various geometric invariants near singular points of such surfaces and curves.

Findings

Gaussian and mean curvatures diverge with specific orders

Geodesic, normal curvatures, and torsion have quantifiable divergence orders

Boundedness of invariants reflects the local geometry near singularities

Abstract

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study boundedness and orders of several geometric invariants near a singular point of a surface which is a suspension of a singular curve in the plane and those of curves passing through the singular point. We evaluates the orders of Gaussian and mean curvatures and them of geodesic, normal curvatures and geodesic torsion for the curve.