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Jacobi's elliptic functions and Lagrangian immersions

Published online by Cambridge University Press:  14 November 2011

Bang-Yen Chen
Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027, U.S.A. e-mail: [email protected]
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Abstract

First, we establish a sharp inequality between the squared mean curvature and the scalar curvature for a Lagrangian submanifold in a nonflat complex-space-form. Then, by utilising the Jacobi's elliptic functions en and dn, we introduce three families of Lagrangian submanifolds and two exceptional Lagrangian submanifolds Fn, Ln in nonflat complex-space-forms which satisfy the equality case of the inequality. Finally, we obtain the complete classification of Lagrangian submanifolds in nonflat complex-space-forms which satisfy this basic equality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 4 , 1996 , pp. 687 - 704
Copyright
Copyright © Royal Society of Edinburgh 1996

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