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Gauss-Bonnet theorem (Theorem)

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

$\displaystyle \int_S K=2\pi\,\chi(S), $
where $ K$ is the Gaussian curvature of $ S$ and $ \chi(S)$ its Euler-Poincaré characteristic.



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"Gauss-Bonnet theorem" is owned by Simone. [ full author list (4) ]
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Cross-references: Gaussian curvature, boundary, surface, orientable, compact
There are 4 references to this entry.

This is version 4 of Gauss-Bonnet theorem, born on 2007-01-26, modified 2007-04-28.
Object id is 8824, canonical name is GaussBonetTheorem.
Accessed 1037 times total.

Classification:
AMS MSC: 53A05 (Differential geometry :: Classical differential geometry :: Surfaces in Euclidean space)
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Duplicate by PrimeFan on 2007-01-26 17:04:22
This is a duplicate of the much-maligned object 8807, which has pretty much the same content plus slightly more detail.
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