Real hypersurfaces in [formula omitted] with constant Reeb sectional curvature

Abstract

We prove that the structure Jacobi operator Rξ on a real hypersurface M in the complex projective space CP2 satisfies Rξ+κϕ2=0 with κ∈R⁎ (or equivalently, constant Reeb sectional curvature) if and only if either M is of type (A) or M is locally congruent to a non-homogeneous Hopf hypersurface with vanishing Hopf principal curvature.