Recurrent Jacobi operator of real hypersurfaces in complex two-plane Grassmannians (Q2856995)

The authors introduce the following notion. A real hypersurface \(M\) in the complex two-plane Grassmannian \(G_2 (\mathbb{C}^{m+2} )\) with a recurrent normal Jacobi operator is defined by NEWLINE\[NEWLINE (\nabla _X \overline{R} _N )(Y)= \omega (X) \overline{R}_N (Y), NEWLINE\]NEWLINE where \(\overline{R}\) is the curvature tensor, \(\omega\) denotes a 1-form on \(M\), \(X\), \(Y\) are any tangent vector fields to \(M\), and \(N\) is a unit normal vector field.NEWLINENEWLINENEWLINEThe main result states: There does not exist any Hopf hypersurface in complex two-plane Grassmannians \(G_2 (\mathbb{C}^{m+2} )\) with recurrent normal Jacobi operator.