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

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Author(s): Carlos J. G. Machado | Juan de Dios Pérez | Young Jin Suh

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 01;
Issue: 03;
Start page: 67;
Date: 2011;
Original page

Keywords: Real Hypersurfaces | Complex Two-Plane Grassmannians | Jacobi Operators | Codazzi Type

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.
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