
The authors define a quasi Einstein manifold to be a non-flat Riemannian manifold \((M^n,g)\), \(n>2\), such that its Ricci tensor \(S\) satisfies the condition \( S(X,Y)=a g(X,Y) + b A(X) A(Y), \) where \(a,b\neq 0\) are associated scalars and \(A\) is a non-zero associated 1-form such that \(g(X,U)=A(X)\), \(g(U,U)=1\). The associated scalars and 1-form are used to describe some properties of quasi Einstein manifolds. Namely conditions for \(M\) to be conformally conservative are described.
Special Riemannian manifolds (Einstein, Sasakian, etc.), conformally conservative manifold, quasi-Einstein manifold
Special Riemannian manifolds (Einstein, Sasakian, etc.), conformally conservative manifold, quasi-Einstein manifold
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