scholarly journals Levi-Flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

2019 ◽  
Author(s):  
Robert L. Bryant
Keyword(s):  
Complex Space ◽  
Two Dimensional ◽  
Space Forms ◽  
Minimal Hypersurfaces ◽  
Complex Space Forms

Derivatives on Real Hypersurfaces of Two-Dimensional Non-flat Complex Space Forms

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Two Dimensional ◽  
Space Forms ◽  
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.

Symplectic critical surfaces with parallel normalized mean curvature vector in two-dimensional complex space forms

2019 ◽  
Vol 30 (05) ◽  
pp. 1950027 ◽  
Author(s):  
Ling He ◽  
Jiayu Li
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Curvature Vector ◽  
Necessary Condition ◽  
Holomorphic Sectional Curvature ◽  
Critical Surface ◽  
Mean Curvature Vector ◽  
Two Dimensional ◽  
Space Forms ◽  
Complex Space Forms

In this paper, we obtain a sufficient and necessary condition for the existence of symplectic critical surfaces with parallel normalized mean curvature vector in two-dimensional complex space forms. Explicitly, we find that there does not exist any symplectic critical surface with parallel normalized mean curvature vector in two-dimensional complex space forms of nonzero constant holomorphic sectional curvature. And there exists and only exists a two-parameters family of symplectic critical surfaces with parallel normalized mean curvature vector in two-dimensional complex plane, which are rotationally symmetric.

scholarly journals Isoparametric submanifolds in two-dimensional complex space forms

2017 ◽  
Vol 53 (2) ◽  
pp. 205-216 ◽  
Author(s):  
José Carlos Díaz-Ramos ◽  
Miguel Domínguez-Vázquez ◽  
Cristina Vidal-Castiñeira
Keyword(s):  
Complex Space ◽  
Two Dimensional ◽  
Space Forms ◽  
Isoparametric Submanifolds ◽  
Complex Space Forms
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