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References
A recent survey about umbilics on surfaces is Gutierrez, C. and Sotomayor, J., Lines of curvature, umbilic points and Carathéodory conjecture. Resen. Inst. Mat. Estat. Univ. Sao Paulo, Vol. 3, No. 3, 291–322, 1998. The proof for the analytical case can be found in Ivanov, V.V., The analytic conjecture of Carathéodory, Siberian Math. J., v. 43, 251–322, 2002.
Über einige Eigenschaften der Flächen mit konstantem Krümmungsmasz, Crelles J., v. 88, 68–73, 1880.
Comptes Rendus, v. 134, 740–743, 1902.
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(2006). Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space. In: Rovenski, V.Y. (eds) Differential Geometry of Curves and Surfaces. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4402-4_2
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DOI: https://doi.org/10.1007/0-8176-4402-4_2
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