scholarly journals Lie derivatives and structure Jacobi operator on real hypersurfaces in complex projective spaces II

2020 ◽  
Vol 73 ◽  
pp. 101685
Author(s):  
Juan de Dios Pérez ◽  
David Pérez-López
Keyword(s):  
Jacobi Operator ◽  
Projective Spaces ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Lie Derivatives ◽  
Complex Projective Spaces ◽  
Complex Projective

Lie and generalized Tanaka–Webster derivatives on real hypersurfaces in complex projective spaces

2014 ◽  
Vol 25 (12) ◽  
pp. 1450115 ◽  
Author(s):  
Juan de Dios Pérez
Keyword(s):  
Complex Projective Space ◽  
Jacobi Operator ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Structure Jacobi Operator ◽  
Complex Projective Spaces ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Complex Projective

On a real hypersurface M in complex projective space we can consider the Levi-Civita connection and for any nonnull constant k the kth g-Tanaka–Webster connection. We classify real hypersurfaces such that both the Lie derivative associated to the Levi-Civita connection and the kth g-Tanaka–Webster derivative in the direction of the structure vector field ξ coincide when we apply them to either the shape operator or the structure Jacobi operator of M.

Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie 𝔻-parallel

2013 ◽  
Vol 56 (2) ◽  
pp. 306-316 ◽  
Author(s):  
Juan de Dios Pérez ◽  
Young Jin Suh
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Jacobi Operator ◽  
Real Hypersurfaces ◽  
Structure Jacobi Operator ◽  
Complex Projective

AbstractWe prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie 𝔻-parallel and satisfies a further condition.

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