Real hypersurfaces in complex two-plane Grassmannians with commuting restricted Jacobi operators

2014/09/25 by Eunmi Pak, Young Jin Suh, Pak, Eunmi +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1409.7177

arxiv created 2014/09/25 · arxiv updated 2014/09/26

Abstract

In this paper, we have considered a new commuting condition, that is, (R_ξϕ) S = S (R_ξϕ) (resp. (\BarR_Nϕ) S = S (\BarR_Nϕ)) between the restricted Jacobi operator~R_ξϕ (resp. \BarR_Nϕ), and the Ricci tensor S for real hypersurfaces M in G₂(\mathbb C^m+2). In terms of this condition we give a complete classification for Hopf hypersurfaces M in G₂(\mathbb C^m+2).

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