Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 from minimal surfaces in 𝕊3
2018 ◽
Vol 149
(03)
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pp. 655-689
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Keyword(s):
AbstractWe study non-totally geodesic Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 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 𝕊3. 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.
2007 ◽
Vol 50
(3)
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pp. 321-333
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Keyword(s):
1994 ◽
Vol 209
(1)
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1983 ◽
Vol 6
(2)
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pp. 341-361
2019 ◽
Vol 2019
(753)
◽
pp. 159-191
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2009 ◽
Vol 194
◽
pp. 149-167
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