Int. Journal of Math. Analysis, Vol. 5, 2011, no. 12, 559 - 568 On Quasi-Conformally Flat Quasi-Einstein Spaces with Recurrent Curvature Absos Ali Shaikh and Ananta Patra Department of Mathematics University of Burdwan, Golapbag Burdwan-713 104 West Bengal, India aask2003@yahoo.co.in Abstract The present paper deals with a study of quasi-conformally flat quasi- Einstein spaces with recurrent curvature. We obtain various necessary and sufficient conditions for such a space to be recurrent (resp. concicu- larly recurrent, projectively recurrent and conformally recurrent). Also the existence of a quasi-Einstein space is ensured by an example which is neither quasi-conformally flat nor quasi-conformally symmetric . Mathematics Subject Classification: 53B30, 53B50, 53C15. Keywords: quasi-Einstein space, quasi-conformally flat, recurrent space, concircular curvature tensor, projective curvature tensor 1 Introduction The notion of quasi-Einstein spaces arose during the study of exact solu- tions of the Einstein field equations as well as during considerations of quasi- umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein spaces. It is well known that a connected Riemannian space (M n ,g ),n> 2, is Einstein if its Ricci tensor R ij of type (0, 2) is of the form R ij = αg ij , where α is a constant, which turns into R ij = R n g ij , R being the scalar curvature (constant) of the space. Let (M n ,g ),n> 2, be a connected Riemannian space. Let U = {x ∈ M : R ij = R n g ij at x}. Then (M n ,g ) is said to be quasi-Einstein space ([2],[10], [11]) if on U ⊂ M , the relation R ij - αg ij = βA i A j (1)