Definition:Integral Curvature

Definition

Let $ABC$ be a geodesic triangle on a surface $S$.

The integral curvature of $ABC$ is given by:

$\ds \int_{ABC} \Kappa \rd a$

where $\Kappa$ is the Gaussian curvature at each point on $ABC$.

Historical Note

The concept of integral curvature was developed by Carl Friedrich Gauss in his $1827$ work Disquisitiones Generales circa Superficies Curvas.

Sources

• Weisstein, Eric W. "Integral Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IntegralCurvature.html