Ruled Lagrangian Submanifolds of the 6-Sphere

Details Ruled Lagrangian Submanifolds of the 6-Sphere Ruled Lagrangian Submanifolds of the 6-Sphere

2008-07-14

arxiv.org/abs/0807.2084v2

Transactions of the American Mathematical Society 363 (2011), 2305-2339

Mathematics

Differential Geometry

46 pages, v2: minor corrections, version to appear in Trans. Amer. Math. Soc

Scientific paper

10.1090/S0002-9947-2010-05167-0

This article sets out to serve a dual purpose. On the one hand, we give an explicit description of the Lagrangian submanifolds of the nearly Kaehler 6-sphere which are ruled by circles of constant radius using Weierstrass formulae. On the other, we recognise all previous known examples of these Lagrangians as being ruled by such circles. Therefore, we describe all families of Lagrangians in the 6-sphere whose second fundamental form satisfies natural pointwise conditions: so-called second order families.

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