The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms

2000 ◽  
Vol 122 (2) ◽  
pp. 295-317 ◽  
Author(s):  
K. (Katsuei) Kenmotsu ◽  
Detang Zhou
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Two Dimensional ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
Parallel Mean Curvature ◽  
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 Totally real submanifolds of a complex space form

1996 ◽  
Vol 19 (1) ◽  
pp. 39-44 ◽  
Author(s):  
U-Hang Ki ◽  
Young Ho Kim
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Complex Space Form ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Real Submanifolds ◽  
Parallel Mean Curvature ◽  
Totally Real

Totally real submanifolds of a complex space form are studied. In particular, totally real submanifolds of a complex number space with parallel mean curvature vector are classified.

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