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Annals of Global Analysis and Geometry

, Volume 34, Issue 1, pp 1–20 | Cite as

The denominators of Lagrangian surfaces in complex Euclidean plane

  • Katsuhiro MoriyaEmail author
Original Paper

Abstract

A quotient of two linearly independent quaternionic holomorphic sections of a quaternionic holomorphic line bundle over a Riemann surface is a conformal branched immersion from a Riemann surface to four-dimensional Euclidean space. On the assumption that a quaternionic holomorphic line bundle is associated with a Lagrangian-branched immersion from a Riemann surface to complex Euclidean plane, we shall classify the denominators of Lagrangian-branched immersion from a Riemann surface to complex Euclidean plane.

Keywords

Lagrangian surface Quaternionic holomorphic vector bundle  The Carleman-Bers-Vekua system 

Mathematics Subject Classification (2000)

Primary 53D12 Secondary 53C42 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TsukubaIbaraki-kenJapan

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