Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature

This paper contains a proof of the unbendability of a closed surface of genus $p>1$ and positive extrinsic curvature in a $3$-dimensional Riemannian space, and the unbendability of a closed surface of genus $p=1$ and positive extrinsic curvature in a Riemannian space when one point of the surface is fixed.
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