scholarly journals Lagrangian submanifolds in 3-dimensional complex space forms with isotropic cubic tensor

2011 ◽  
Vol 18 (3) ◽  
pp. 431-451 ◽  
Author(s):  
Xianfeng Wang ◽  
Haizhong Li ◽  
Luc Vrancken
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
3 Dimensional ◽  
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 On 3-dimensional contact slant submanifolds in Sasakian space forms

2003 ◽  
Vol 68 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Sharp Inequality ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
3 Dimensional ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Complex Space Forms

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.

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