On space-like Kähler submanifolds with \(RS=0\) in an indefinite complex space form (Q699957)

The authors consider (semi-definite) Kähler manifolds and complete space-like complex submanifolds in indefinite complex hyperbolic spaces. They impose the condition of semi-symmetric type \(RS = 0\), where \(S\) is the Ricci tensor and the curvature tensor \(R\) acts like a derivation. Under these hypothesis, some additional sufficient conditions are found, in order that the Kähler manifolds and the corresponding submanifolds are Einstein manifolds.