Gauss-Bonnet theorem for surfaces without boundary

If $S$ is a compact, orientable surface without boundary, then

$${\int }_{S}K=2\pi \chi (S),$$

where $K$ is the Gaussian curvature of $S$ and $\chi (S)$ its Euler-Poincaré characteristic. (http://planetmath.org/EulerrCharacteristic)

Title	Gauss-Bonnet theorem for surfaces without boundary
Canonical name	GaussBonnetTheoremForSurfacesWithoutBoundary
Date of creation	2013-03-22 16:37:30
Last modified on	2013-03-22 16:37:30
Owner	Simone (5904)
Last modified by	Simone (5904)
Numerical id	8
Author	Simone (5904)
Entry type	Theorem
Classification	msc 53A05