On \(K\)-contact \(\eta\)-Einstein manifolds (Q2733928)

Let \((M^n,g)\) be a contact Riemannian manifold with contact form \(\eta\), associated vector field \(\xi\), (1,1)-tensor field \(\varphi\) and associated Riemannian metric \(g\). If \(\xi\) is a Killing vector field, then \(M^n\) is called a \(K-\)contact Riemannian manifold. A \(K\)-contact manifold \(M^n\) is said to be \(\eta\)-Einstein if its Ricci tensor \(S\) is of the form \(S=ag+b\eta \times \eta\), where \(a\), \(b\) are smooth functions on \(M^n\). The purpose of this note is to study a \(K\)-contact \(\eta\)-Einstein manifold satisfying certain conditions on the curvature tensor.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].