Singh, J. P. On an Einstein \(M\)-projective \(P\)-Sasakian manifolds. (English) Zbl 1201.53036 Bull. Calcutta Math. Soc. 101, No. 2, 175-180 (2009). Summary: We prove that if in an Einstein \(P\)-Sasakian manifold \(R(T,X)\cdot W^*=0\) holds, then it is locally isometric with \(S^n(1)\). It is also proved that an \(n\)-dimensional \(\eta\) Einstein \(P\)-Sasakian manifold \(M\) satisfies \(W^*(T,X)\cdot R=0\) if an only if either \(M^n\), is locally isometric to the hyperbolic space \(H^n(-1)\) or the scalar curvature \(\mathfrak r\) of \(M^n\) is \(r=-n(n-1)\). Cited in 1 Document MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:Einstein \(P\)-Sasakian manifold; locally isometric; hyperbolic space PDFBibTeX XMLCite \textit{J. P. Singh}, Bull. Calcutta Math. Soc. 101, No. 2, 175--180 (2009; Zbl 1201.53036)