Real 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.

Keywords:

complex space form, real hypersurface, structure Jacobi operator complex space form, real hypersurface, structure Jacobi operator

MSC Classifications:

53B20, 53C15, 53C25 show english descriptions Local Riemannian geometry
General geometric structures on manifolds (almost complex, almost product structures, etc.)
Special Riemannian manifolds (Einstein, Sasakian, etc.) 53B20 - Local Riemannian geometry
53C15 - General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)

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