Real Hypersurfaces in Non-Flat Complex Space form with Structure Jacobi Operator of Lie-Codazzi Type

2015 ◽  
Vol 39 (1) ◽  
pp. 17-27
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Codazzi Type

scholarly journals REAL HYPERSURFACES WITH CYCLIC-PARALLEL STRUCTURE JACOBI OPERATORS IN A NONFLAT COMPLEX SPACE FORM

2009 ◽  
Vol 81 (2) ◽  
pp. 260-273 ◽  
Author(s):  
U-HANG KI ◽  
HIROYUKI KURIHARA
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Complex Space Form ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Jacobi Operators

AbstractIt is known that there are no real hypersurfaces with parallel structure Jacobi operators in a nonflat complex space form. In this paper, we classify real hypersurfaces in a nonflat complex space form whose structure Jacobi operator is cyclic-parallel.

scholarly journals Real hypersurfaces in a complex space form with a condition on the structure Jacobi operator

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
S. Kon ◽  
Tee-How Loo ◽  
Shiquan Ren
Keyword(s):  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Jacobi Operator ◽  
Hyperbolic Spaces ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
The Real ◽  
Complex Projective

AbstractIn this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator R ξ satisfying (∇X R ξ)ξ = 0, for all vector fields X in the maximal holomorphic distribution D. With this result, we prove the non-existence of real hypersurfaces with D-parallel as well as D-recurrent structure Jacobi operator in complex projective and hyperbolic spaces. We can also prove the non-existence of real hypersurfaces with recurrent structure Jacobi operator in a non-flat complex space form as a corollary.

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.

On a Characterization of Real Hypersurfaces of Type a in a Complex Space Form

1994 ◽  
Vol 37 (2) ◽  
pp. 238-244 ◽  
Author(s):  
U-Hang Ki ◽  
Young-Jin Suh
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Type A ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Orthogonal Distribution

AbstractIn this paper, under certain conditions on the orthogonal distribution T0, we give a characterization of real hypersurfaces of type A in a complex space form Mn(c), c ≠ 0.

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