The denominators of Lagrangian surfaces in complex Euclidean plane
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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.
KeywordsLagrangian surface Quaternionic holomorphic vector bundle The Carleman-Bers-Vekua system
Mathematics Subject Classification (2000)Primary 53D12 Secondary 53C42
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