On quasi Einstein manifolds. (English) Zbl 0968.53030

Chaki, M. C.; Maity, R. K.

Publ. Math. Debr. 57, No. 3-4, 297-306 (2000).

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.

Reviewer: Josef Janyska (Brno)

MSC:

53C25

Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

quasi-Einstein manifold; conformally conservative manifold