## Torus and Flat Torus

Torus

One can calculate the Gauss curvature by the following formula

In fact

So one can see that some places is positive and some places is negative. There is another torus homeomorphic to this one, which is also with different metric,

lies in the space . Using the formula above, one can get

So this torus has a name as flat torus. Flat torus can not be put in because the following therem:

**Theorem:** On every compact surface there is some point with .

**Remark:**Oprea, John. Differential geometry and its applications. p129

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