Geodesic
Real hypersurfaces in a complex projective space with pseudo-${\mathbb D}$-parallel structure Jacobi operator
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1025-1036.

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We introduce the new notion of pseudo-$\mathbb D $-parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces.
Classification : 53B25, 53C15
Keywords: real hypersurface; structure Jacobi operator 
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     title = {Real hypersurfaces in a complex projective space with pseudo-${\mathbb D}$-parallel structure {Jacobi} operator},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1025--1036},
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Lee, Hyunjin; Pérez, Juan de Dios; Suh, Young Jin. Real hypersurfaces in a complex projective space with pseudo-${\mathbb D}$-parallel structure Jacobi operator. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1025-1036. http://geodesic.mathdoc.fr/item/CMJ_2010__60_4_a9/