Invariance of the distributional curvature of the cone under smooth diffeomorphisms

TL;DR

This paper demonstrates that the distributional curvature of a 2-cone, computed via Colombeau's generalized functions, remains unchanged under smooth coordinate transformations, highlighting its invariance property.

Contribution

It provides an explicit calculation proving the invariance of distributional curvature of a 2-cone under smooth diffeomorphisms using Colombeau's generalized functions.

Findings

Distributional curvature of a 2-cone is invariant under smooth transformations.

Explicit calculation confirms invariance using Colombeau's framework.

Supports the robustness of distributional curvature in geometric analysis.

Abstract

An explicit calculation is carried out to show that the distributional curvature of a 2-cone, calculated by Clarke et al. (1996), using Colombeau's new generalised functions is invariant under non-linear $C^\infty$ coordinate transformations.