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.

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.

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.

LEVI-UMBILICAL REAL HYPERSURFACES IN A COMPLEX SPACE FORM

2016 ◽  
Vol 229 ◽  
pp. 99-112 ◽  
Author(s):  
JONG TAEK CHO ◽  
MAKOTO KIMURA
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Levi Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Complex Projective Plane ◽  
Nonzero Constant ◽  
Local Construction ◽  
Complex Projective

We give a classification of Levi-umbilical real hypersurfaces in a complex space form $\widetilde{M}_{n}(c)$, $n\geqslant 3$, whose Levi form is proportional to the induced metric by a nonzero constant. In a complex projective plane $\mathbb{C}\mathbb{P}^{2}$, we give a local construction of such hypersurfaces and moreover, we give new examples of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^{2}$.

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