Complete nonorientable minimal surfaces in 𝑅³

Ishihara, Tōru

doi:10.1090/S0002-9947-1992-1064269-5

Complete nonorientable minimal surfaces in $\textbf {R}^ 3$
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Trans. Amer. Math. Soc. 333 (1992), 889-901 Request permission

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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