scholarly journals The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms

2016 ◽  
Vol 39 (1) ◽  
pp. 154-174
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Jacobi Operator ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Complex Space Forms

scholarly journals Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Vector Field ◽  
Hyperbolic Space ◽  
Complex Space ◽  
Jacobi Operator ◽  
Three Dimensional ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Complex Space Forms

AbstractIn this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.

Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator

2008 ◽  
Vol 51 (3) ◽  
pp. 359-371 ◽  
Author(s):  
Jong Taek Cho ◽  
U-Hang Ki
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Symmetric Structure ◽  
Complex Space Forms ◽  
Complex Projective

AbstractReal hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type (A) in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator.

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