Real hypersurfaces with pseudo-parallel normal Jacobi operator in complex two-plane Grassmannians

2014/02/24 by Avik De, De, Avik, Tee‐How Loo +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 53C40 53B25 #Secondary 53C15 #math.DG #msc:53B25 #msc:53C15 #msc:53C40

paper · pdf · doi:10.48550/arxiv.1402.5705

arxiv created 2014/02/24 · openalex publication_date 2014/02/24 · arxiv updated 2014/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The objective of the present paper is to prove the non-existence of real hypersurface with pseudo-parallel normal Jacobi operator in complex two-plane Grassmannians. As a corollary, we show that there does not exist any real hypersurface with semi-parallel or recurrent normal Jacobi operator in complex two-plane Grassmannians. This answers a question considered in [Monatsh Math, 172 (2013), 167-178] in negative.

Related

• Real hypersurfaces in complex Grassmannians of rank two with semi-parallel structure Jacobi operator
• Semi-parallel real hypersurfaces in complex two-plane Grassmannians
• Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians
• Real hypersurfaces equipped with pseudo-parallel structure Jacobi operator in CP² and CH²
• Real Hypersurfaces in CP² AND CH² whose structure Jacobi operator is Lie D-parallel