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

2012/10/06 by Κωνσταντίνα Παναγιωτίδου, Konstantina Panagiotidou, Panagiotidou, Konstantina +2
Mathematics · Physics and Astronomy · #53C15 #53C40 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53C15 #msc:53C40

paper · pdf · doi:10.48550/arxiv.1210.1937

11 pages

arxiv created 2012/10/06 · openalex publication_date 2012/10/06 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved the non-existence of Hopf hypersurfaces in G₂(\Bbb 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 \frak D or its orthogonal complement \frak D^\bot is invariant by the shape operator.

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