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Transactions of the American Mathematical Society

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

 

 

Complete nonorientable minimal surfaces in $ {\bf R}\sp 3$


Author: Tōru Ishihara
Journal: Trans. Amer. Math. Soc. 333 (1992), 889-901
MSC: Primary 53A10; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9947-1992-1064269-5
MathSciNet review: 1064269
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Abstract: We will study complete minimal immersions of nonorientable surfaces into $ {R^3}$. Especially, we construct a nonorientable surface $ {P_2}$ which is homeomorphic to a Klein bottle and show that for any integer $ m \geq 4$, there are complete minimal immersion of $ M = {P_2} - \{ q\} $, $ q \in {P_2}$ in $ {R^3}$ with one end and total curvature $ C(M) = - 4m\pi $.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1064269-5
Article copyright: © Copyright 1992 American Mathematical Society