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edited Dec 14, 2019 at 5:43

Flat metric on compact surface minus a point

Let $T^2$ be a compact smooth surface and let $p\in T^2$. Suppose that $T^2$ admits a symmetric $\left(0,2\right)$-tensor which is a flat Riemannian metric restricted to $T^2-\{p\}$. Is it true that $\chi(T)=0$?

dg.differential-geometry surfaces

asked Dec 14, 2019 at 5:12

Gianni del Fiore