Geodesic
Possible generalizations of the Minagawa--Rado Lemma on the rigidity of a~surface of revolution with a~fixed parallel
Matematičeskie zametki, Tome 19 (1976) no. 1, pp. 123-132.

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A general necessary and sufficient criterion is established for the rigidity of a surface of revolution $S\in C^1$ under the condition of a fixed parallel. Also two simple sufficient criteria for this property are given. It is shown by an example that this property does not hold for $S\in C^1$ in the general case. 
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     author = {I. Kh. Sabitov},
     title = {Possible generalizations of the {Minagawa--Rado} {Lemma} on the rigidity of a~surface of revolution with a~fixed parallel},
     journal = {Matemati\v{c}eskie zametki},
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     number = {1},
     year = {1976},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_1_a14/}
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I. Kh. Sabitov. Possible generalizations of the Minagawa--Rado Lemma on the rigidity of a~surface of revolution with a~fixed parallel. Matematičeskie zametki, Tome 19 (1976) no. 1, pp. 123-132. http://geodesic.mathdoc.fr/item/MZM_1976_19_1_a14/