Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type

We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Two-plane Grassmannians

We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.

Real Hypersurfaces in <i>CP²</i>and <i>CH²</i>Equipped With Structure Jacobi Operator Satisfying L_ξl =▽_ξl

Recently in [1], Perez and Santos classified real hypersurfaces in complex projective space CPn for n ≥ 3, whose Lie derivative of structure Jacobi operator in the direction of the structure vector field coincides with the covariant derivative of it in the same direction. The present paper completes the investigation of this problem studying the case n = 2 in both complex projective and hyperbolic spaces.