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.

Pseudo-anti commuting Ricci tensor for real hypersurfaces in the complex hyperbolic quadric

We introduce a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the noncompact complex hyperbolic quadric Q^(m?)= SO_2~0,_m/SO_2SO_m and give a complete classi?cation of these hypersurfaces.

Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster D-Parallel Shape Operator

In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.

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.