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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Principal lines on surfaces immersed with constant mean curvature


Authors: C. Gutiérrez and J. Sotomayor
Journal: Trans. Amer. Math. Soc. 293 (1986), 751-766
MSC: Primary 53A10; Secondary 58F18
DOI: https://doi.org/10.1090/S0002-9947-1986-0816323-5
MathSciNet review: 816323
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Abstract: Configurations of lines of principal curvature on constant mean curvature immersed surfaces are studied. Analytical models for these configurations near general isolated umbilical points and particular types of ends are found. From the existence of transversal invariant measures for the foliations by principal lines, established here, follows that the union of recurrent lines of principal curvature is an open set. Examples illustrating all possible cases are given.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0816323-5
Keywords: Principal lines, constant mean curvature surfaces, umbilical points, ends, quadratic differentials, transversal measures
Article copyright: © Copyright 1986 American Mathematical Society