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Ruled Lagrangian submanifolds of the 6-sphere


Author: Jason D. Lotay
Journal: Trans. Amer. Math. Soc. 363 (2011), 2305-2339
MSC (2010): Primary 53B20, 53B25
DOI: https://doi.org/10.1090/S0002-9947-2010-05167-0
Published electronically: November 30, 2010
MathSciNet review: 2763718
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Abstract: This article sets out to serve a dual purpose. On the one hand, we give an explicit description of the Lagrangians in the nearly Kähler 6-sphere $ \mathcal{S}^6$ which are ruled by circles of constant radius using `Weierstrass formulae'. On the other hand, we recognise all known examples of these Lagrangians as being ruled by such circles. Therefore, we describe all families of Lagrangians in $ \mathcal{S}^6$ whose second fundamental form satisfies natural pointwise conditions--the so-called `second order families'.


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Additional Information

Jason D. Lotay
Affiliation: Department of Mathematics, Imperial College, London, SW7 2RH, United Kingdom
Email: jlotay@imperial.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2010-05167-0
Received by editor(s): August 22, 2008
Published electronically: November 30, 2010
Article copyright: © Copyright 2010 American Mathematical Society

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