Addendum to the paper “Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor”

Abstract

In this paper, we introduce some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 ( C m + 2 ) , namely, F -invariant and invariant Ricci tensor. Using these notions, we give non-existence theorem and characterization for the special case among the real hypersurfaces of Type ( A ) in G 2 ( C m + 2 ) , respectively. Here the distribution F is defined by F = [ ξ ] ∪ D ⊥ where D ⊥ = Span { ξ 1 , ξ 2 , ξ 3 } and [ ξ ] = Span { ξ } .