Does the tangential rotation term $ \int k_g ds $ of Gauss-Bonnet theorem ( for continuous or discontinuous lines on a surface) have a name or symbol in differential geometry ?
The second term $ \int K dA $ integral curvature and the topological invariant Euler characteristic have identifiable names.
EDIT1:
$ \int k_g ds $, the 'Boundary Rotation' if you will, is defined here for tangent developable Frills with zero Gauss curvature. They are $ 2 \pi $ for flat disc rim, 4 EllipticE(-1/2) for the Viviani Frill and favorite 'Twisted Frill1' of mine, 8 EllipticE(-1/4).They are tangential to the North-South Polar axis. Can be made by cutting and pasting flexible rings of Boundary Rotation $ >2 \pi.$
Appreciate anyone coming up with paper/thin plastic models to post it here.
