Let M be a semi-invariant submanifold with almost contact metric structure (ϕ,ξ,η,g) of codimension 3 in a complex space form Mn+1(c) for c≠0. We denote by S and Rξ be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector ξ, respectively. Suppose that the third fundamental form t satisfies dt(X,Y)=2θg(ϕX,Y) for a certain scalar θ≠2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies Rξϕ=ϕRξ and at the same time Sξ=g(Sξ,ξ)ξ, then M is a real hypersurface in Mn(c) (⊂Mn+1(c)) provided that r¯−2(n−1)c≤0, where r¯ denotes the scalar curvature of M.

Keywords: semi-invariant submanifold, distinguished normal, complex space form, structure Jacobi operator, Ricci tensor, Hopf hypersurfaces