scholarly journals Quasi-biharmonic Lagrangian surfaces in Lorentzian complex space forms

2011 ◽  
Vol 192 (2) ◽  
pp. 191-201 ◽  
Author(s):  
Toru Sasahara
Keyword(s):  
Complex Space ◽  
Space Forms ◽  
Lagrangian Surfaces ◽  
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.

scholarly journals Biharmonic and Quasi-Biharmonic Slant Surfaces in Lorentzian Complex Space Forms

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yu Fu
Keyword(s):  
Complex Space ◽  
Space Forms ◽  
Trapped Surfaces ◽  
Lagrangian Surfaces ◽  
Marginally Trapped Surfaces ◽  
Complex Space Forms

In 1991, Chen and Ishikawa initially studied biharmonic marginally trapped surfaces in neutral pseudo-Euclidean 4-space. Recently, biharmonic and quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms were studied by Sasahara in 2007 and 2011, respectively. In this paper we extend Sasahara's results to the case of slant surfaces in Lorentzian complex space forms. By results, we completely classify biharmonic marginally trapped slant surfaces and quasi-biharmonic marginally trapped slant surfaces in Lorentzian complex space forms.

scholarly journals BIHARMONIC LAGRANGIAN SURFACES OF CONSTANT MEAN CURVATURE IN COMPLEX SPACE FORMS

2007 ◽  
Vol 49 (3) ◽  
pp. 497-507 ◽  
Author(s):  
TORU SASAHARA
Keyword(s):  
Mean Curvature ◽  
Euclidean Plane ◽  
Complex Space ◽  
Constant Mean Curvature ◽  
Space Forms ◽  
Lagrangian Surfaces ◽  
Complex Space Forms

AbstractBiharmonic Lagrangian surfaces of constant mean curvature in complex space forms are classified. A further important point is that new examples of marginally trapped biharmonic Lagrangian surfaces in an indefinite complex Euclidean plane are obtained. This fact suggests that Chen and Ishikawa's classification of marginally trapped biharmonic surfaces [6] is not complete.

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