On generalised Ricci-recurrent Lorentzian para-Sasakian manifold (Q2583492)

The paper under review extends the results given recently by \textit{N. Guha} [Bull. Calcutta Math. Soc. 92, No.~2, 361--364 (2000; Zbl 0992.53032)] in case of a generalized Ricci-recurrent Sasakian manifold. More precisely, it is shown that in a generalized Ricci-recurrent Lorentzian para-Sasakian manifold \(M\) if its Ricci tensor \(S\) satisfies the condition \((\nabla x S)(Y, Z)=A(X)S(Y,Z)+ B(X)g(Y,Z)\), \(A\), \(B\) are 1-forms, the vector fields \(P\) and \(Q\) such that \(g(X,P) = A(X)\) and \(g(X,Q) = B(X)\), have the opposite directions. Also, it is shown that if \(S\) satisfies \((\nabla_X S)(Y,Z)+ \nabla_Y S)(Z,X)+(\nabla_Z S)(X,Y )=0\), then \(M\) is an Einstein manifold.