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.
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Moriya, K. The denominators of Lagrangian surfaces in complex Euclidean plane. Ann Glob Anal Geom 34, 1–20 (2008). https://doi.org/10.1007/s10455-007-9100-x
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DOI: https://doi.org/10.1007/s10455-007-9100-x