Geodesic
Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature
Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 361-372

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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. Bibliography: 8 titles. 
@article{SM_1976_30_3_a5,
     author = {V. T. Fomenko and S. B. Klimentov},
     title = {Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature},
     journal = {Sbornik. Mathematics},
     pages = {361--372},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/}
}
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V. T. Fomenko; S. B. Klimentov. Nonbendability of closed surfaces of genus $p\geqslant1$ and positive extrinsic curvature. Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 361-372. http://geodesic.mathdoc.fr/item/SM_1976_30_3_a5/