Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator
A real hypersurface \(M\) in a complex two-plane Grassmannians \(G_{2}({\mathbb C}^{m+2})\) is a Hopf recurrent hypersurface if the Hopf foliation of \(M\) is totally geodesic and the shape operator \(A\) satisfies the recurrence relation \[ (\nabla _{X}A)Y=\omega (X)AY \] for a nonzero recurrence \(1\)-form \(\omega \). In this paper, the authors prove that there exist no Hopf recurrent hypersurfaces in the complex two-plane Grassmannians \(G_{2}({\mathbb C}^{m+2})\), \(m\geq 3\).
scientific article; zbMATH DE number 5899041