TITLE:
Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type
AUTHORS:
Carlos J. G. Machado, Juan de Dios Pérez, Young Jin Suh
KEYWORDS:
Real Hypersurfaces, Complex Two-Plane Grassmannians, Jacobi Operators, Codazzi Type
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.1 No.3,
June
3,
2011
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.