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MR1367257 53C45 (53A05)
Toponogov, V. A. On conditions for the existence of umbilical points on a convex surface. (Russian) Sibirsk. Mat. Zh. 36 (1995), no. 4, 903--910, {\rm iv}; translation in Siberian Math. J. 36 (1995), no. 4, 780–786
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