Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians

It is proved the non-existence of Hopf hypersurfaces in G 2 ( C m + 2 ) , m ≥ 3 , whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field in the maximal quaternionic subbundle D or its orthogonal c...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2013-11, Vol.172 (2), p.167-178
Main Authors: Panagiotidou, Konstantina, Tripathi, Mukut Mani
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:It is proved the non-existence of Hopf hypersurfaces in G 2 ( C m + 2 ) , m ≥ 3 , whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field in the maximal quaternionic subbundle D or its orthogonal complement D ⊥ is invariant by the shape operator.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-013-0553-7