scholarly journals Pseudo-symmetries of generalized Wintgen ideal Lagrangian submanifolds

2018 ◽  
Vol 103 (117) ◽  
pp. 181-190
Author(s):  
Miroslava Petrovic-Torgasev ◽  
Anica Pantic
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Ambient Space ◽  
Space Forms ◽  
Equality Case ◽  
Wintgen Ideal Submanifolds ◽  
Complex Space Forms

Mihai obtained the Wintgen inequality, also known as the generalized Wintgen inequality, for Lagrangian submanifolds in complex space forms and also characterized the corresponding equality case. Submanifolds M which satisfy the equality in these optimal general inequalities are called generalized Wintgen ideal submanifolds in the ambient space ?M. For generalized Wintgen ideal Lagrangian submanifolds Mn in complex space forms ?Mn(4c), we will show some properties concerning different kinds of their pseudosymmetry in the sense of Deszcz.

Ideal Lagrangian immersions in complex space forms

2000 ◽  
Vol 128 (3) ◽  
pp. 511-533 ◽  
Author(s):  
BANG-YEN CHEN
Keyword(s):  
Riemannian Manifold ◽  
Isometric Immersion ◽  
Complex Space ◽  
Space Form ◽  
Lagrangian Submanifolds ◽  
Ambient Space ◽  
Complex Space Form ◽  
Space Forms ◽  
Complex Space Forms

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. In this paper we study Lagrangian immersions in complex space forms which are ideal. We prove that all Lagrangian ideal immersions in a complex space form are minimal. We also determine ideal Lagrangian submanifolds in complex space forms.

scholarly journals BIHARMONIC LAGRANGIAN SUBMANIFOLDS IN KÄHLER MANIFOLDS

2013 ◽  
Vol 55 (2) ◽  
pp. 465-480 ◽  
Author(s):  
SHUN MAETA ◽  
HAJIME URAKAWA
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Sufficient Conditions ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Two Dimensional ◽  
Space Forms ◽  
Lagrangian Surfaces ◽  
Necessary And Sufficient ◽  
Complex Space Forms

AbstractWe give the necessary and sufficient conditions for Lagrangian submanifolds in Kähler manifolds to be biharmonic. We classify biharmonic PNMC Lagrangian H-umbilical submanifolds in the complex space forms. Furthermore, we classify biharmonic PNMC Lagrangian surfaces in the two-dimensional complex space forms.

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