Lagrangian submanifolds of the nearly Kahler S3 x S3 from minimal surfaces in S3

Copyright © Royal Society of Edinburgh 2018. We study non-Totally geodesic Lagrangian submanifolds of the nearly Kähler 3 × 3 for which the projection on the first component is nowhere of maximal rank. We show that this property can be expressed in terms of the so-called angle functions and that such Lagrangian submanifolds are closely related to minimal surfaces in 3. Indeed starting from an arbitrary minimal surface, we can construct locally a large family of such Lagrangian immersions, including one exceptional example. We also show that locally all such Lagrangian submanifolds can be obtained in this way.

Publication year:2019

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Authors:International

Authors from:Higher Education

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