Complex hypersurfaces in an indefinite complex space form (Q1098422)

Let M be a complex hypersurface of index 2s in an \((n+1)\)-dimensional indefinite complex space form of constant holomorphic sectional curvature c(\(\neq 0)\) and of index \(2(s+a),\) where \(a=0\) or 1. The authors prove that M is Einstein if M satisfies \(R(X,Y)\cdot S=0\) where R and S denote the curvature tensor and the Ricci tensor, respectively. They also give some examples of Einstein complex hypersurfaces in an indefinite complex Euclidean space.