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June 2014 A construction of special Lagrangian 3-folds via the generalized Weierstrass representation
Saki OKUHARA
Hokkaido Math. J. 43(2): 175-199 (June 2014). DOI: 10.14492/hokmj/1404229921

Abstract

We show that certain holomorphic loop algebra-valued 1-forms over Riemann surfaces yield minimal Lagrangian immersions into the complex 2-dimensional projective space via the Weierstrass type representation, hence 3-dimensional special Lagrangian submanifolds of ℂ3. A particular family of 1-forms on ℂ corresponds to solutions of the third Painlevé equation which are smooth on (0, +∞).

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Saki OKUHARA. "A construction of special Lagrangian 3-folds via the generalized Weierstrass representation." Hokkaido Math. J. 43 (2) 175 - 199, June 2014. https://doi.org/10.14492/hokmj/1404229921

Information

Published: June 2014
First available in Project Euclid: 1 July 2014

zbMATH: 1296.53156
MathSciNet: MR3229070
Digital Object Identifier: 10.14492/hokmj/1404229921

Subjects:
Primary: 53D12
Secondary: 45G05, 53C38

Rights: Copyright © 2014 Hokkaido University, Department of Mathematics

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Vol.43 • No. 2 • June 2014
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