CLASSIFICATION OF LAGRANGIAN SURFACES OF CONSTANT CURVATURE IN THE COMPLEX EUCLIDEAN PLANE
2005 ◽
Vol 48
(2)
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pp. 337-364
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Keyword(s):
AbstractOne of the most fundamental problems in the study of Lagrangian submanifolds from a Riemannian geometric point of view is the classification of Lagrangian immersions of real-space forms into complex-space forms. In this article, we solve this problem for the most basic case; namely, we classify Lagrangian surfaces of constant curvature in the complex Euclidean plane $\mathbb{C}^2$. Our main result states that there exist 19 families of Lagrangian surfaces of constant curvature in $\mathbb{C}^2$. Twelve of the 19 families are obtained via Legendre curves. Conversely, Lagrangian surfaces of constant curvature in $\mathbb{C}^2$ can be obtained locally from the 19 families.
2015 ◽
Vol 92
◽
pp. 167-180
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2013 ◽
Vol 10
(04)
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pp. 1320006
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Keyword(s):
2007 ◽
Vol 49
(3)
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pp. 497-507
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Keyword(s):
2004 ◽
Vol 34
(2)
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pp. 551-563
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1979 ◽
Vol 02
(1)
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pp. 63-70
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2012 ◽
Vol 30
(1)
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pp. 107-123
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Keyword(s):