The structure Jacobi operator and the shape operator of real hypersurfaces in CP² and CH²

2012/09/01 by Κωνσταντίνα Παναγιωτίδου, K. Panagiotidou, Panagiotidou, K.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.DG

paper · pdf · doi:10.48550/arxiv.1209.0131

Includes basic relations from section 3 of arXiv:1201.2540 in order for the reader to fully understand methodology and results

arxiv created 2012/09/01 · openalex publication_date 2012/09/01 · arxiv updated 2012/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents two results conserning real hypersurfaces in CP² and CH². More precisely, it is proved that real hypersurfaces equipped with structure Jacobi operator satisfying condition L_Xl=∇_Xl, where X is a vector field orthogonal to structure vector field ξ, do not exist. Additional real hypersurfaces equipped with shape operator A satisfying relation L_XA=∇_XA, where X is a vector field orthogonal to ξ, do not exist.

Citations

• Real Hypersurfaces in CP² AND CH² whose structure Jacobi operator is Lie D-parallel

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