scholarly journals Classification of Lagrangian submanifolds in complex space forms satisfying a basic equality involving δ(2,2)

2012 ◽  
Vol 30 (1) ◽  
pp. 107-123 ◽  
Author(s):  
Bang-Yen Chen ◽  
Alicia Prieto-Martín
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
Basic Equality ◽  
Complex Space Forms

Jacobi's elliptic functions and Lagrangian immersions

1996 ◽  
Vol 126 (4) ◽  
pp. 687-704 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Elliptic Functions ◽  
Complete Classification ◽  
Sharp Inequality ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Basic Equality ◽  
Complex Space Forms

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.

scholarly journals Classification of δ(2,n− 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

2018 ◽  
Vol 458 (2) ◽  
pp. 1456-1485 ◽  
Author(s):  
Bang-Yen Chen ◽  
Franki Dillen ◽  
Joeri Van der Veken ◽  
Luc Vrancken
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
Complex Space Forms

Classification of Casorati ideal Lagrangian submanifolds in complex space forms

2019 ◽  
Vol 63 ◽  
pp. 30-49 ◽  
Author(s):  
Mohd. Aquib ◽  
Jae Won Lee ◽  
Gabriel-Eduard Vîlcu ◽  
Dae Won Yoon
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
Complex Space Forms
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