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

Carlos J. G. Machado, Juan de Dios Pérez, Young Jin Suh

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DOI: 10.4236/apm.2011.13015                

Abstract

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.

Keywords

Real Hypersurfaces, Complex Two-Plane Grassmannians, Jacobi Operators, Codazzi Type

Conflicts of Interest

The authors declare no conflicts of interest.

References

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