General theorems
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The statement of the theorem
- Gauss–Bonnet theorem The integral of the Gauss curvature on a compact 2-dimensional Riemannian manifold is equal to 2πχ(M) where χ(M) denotes the Euler characteristic of M. This theorem has a generalization to any compact even-dimensional Riemannian manifold, see generalized Gauss-Bonnet theorem.
- Nash embedding theorems. They state that every Riemannian manifold can be isometrically embedded in a Euclidean spaceR^{n}.
Source: Wikipedia