Classification of Isometric Immersions of Spherical and HCMU Footballs into $\E^{3}$

We study global isometric immersions of rotational metrics with two conical ends into Euclidean three-space. For a metric $g=\mathrm{d}u^2+f(u)^2\mathrm{d}θ^2$ of positive Gauss curvature, we prove that vanishing endpoint traces of the weighted mixed shape coefficient $f^2b$ force every smooth isome