The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms (Q291005)

In the reviewed paper, new results concerning three-dimensional real hypersurfaces in non-flat complex space forms are presented. More precisely, the authors characterize such hypersurfaces which additionally satisfy one of the following conditions: (1) The structure Jacobi operator is of Codazzi type with respect to the generalized Tanaka-Webster connection and commutes with the shape operator. (2) The structure Jacobi operator is \(\eta\)-parallel (\(\eta\)-invariant) and commutes with the shape operator. Moreover, Hopf hypersurfaces and ruled hypersurfaces in non-flat complex space forms of dimension greater than three and satisfying the \(\eta\)-invariance condition are also characterized.