Ruled Lagrangian submanifolds in complex Euclidean 3-space
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Abstract
We show that if ruled Lagrangian submanifold M^3 in 3-dimensional complex Euclidean space is Einstein, then it is flat, provided that the map which gives direction of each ruling has constant rank. Also we give explicit construction of flat ruled Lagrangian submanifolds M^3 in C^3, from some horizontal curves in S^5, such that M^3 is neither totally geodesic nor Riemannian product Σ×R.
Journal
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- Memoirs of the Faculty of Science and Engineering Shimane University Ser. B Mathematical Science
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Memoirs of the Faculty of Science and Engineering Shimane University Ser. B Mathematical Science (44), 17-26, 2011-03
Shimane University