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Closed lines of curvature for Weingarten immersions. (English) Zbl 0638.05035

It is shown that the closed principal curvature lines of a Weingarten surface cover an open set.
Reviewer: G.Thorbergsson

MSC:

53A05 Surfaces in Euclidean and related spaces
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References:

[1] Darboux, G.: Théorie Génerale des Surfaces, Chelsea Pub. Co. 1972. 1 ? Vol. IV, Note 7 2 ? Vol. III, Ch. VII
[2] Gutierrez, C. and Sotomayor, J.: Structurally stable Configurations of Lines of Curvature, Asterisque, 98-99, 1982.
[3] Gutierrez, C. and Sotomayor, J.: Principal Lines on Surfaces Immersed with Constant Mean Curvature, Trans. Amer. Math. Soc.239 (1986), 2. · Zbl 0611.53007
[4] Hartman, P. and Wïnter, A.: Umbilical Points and W-Surfaces. Amer. J. Math.76 (1954).
[5] [Hp] Hopf, H.: Lectures on Differential Geometry in the Large. Springer Lect. Notes in Math. 1000; 1983.
[6] [St] Struik, D.: Lectures on Classical Differential Geometry. Addison Wesley, 1950. · Zbl 0041.48603
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