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Integral Curvature


Given a geodesic triangle (a triangle formed by the arcs of three geodesics on a smooth surface),

 int_(ABC)Kda=A+B+C-pi.

Given the Euler characteristic chi,

 intintKda=2pichi,

so the integral curvature of a closed surface is not altered by a topological transformation.


See also

Gauss-Bonnet Formula, Geodesic Triangle

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Cite this as:

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

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