Ricci solitons on locally conformally flat hypersurfaces in space forms

We study Ricci solitons on locally conformally flat hypersurfaces M-n in space forms (M) over tilde (n+1)(c) of constant sectional curvature c with potential vector field a principal curvature eigenvector of multiplicity one. We show that in Euclidean space, M-n is a hypersurface of revolution given in terms of a solution of some non-linear ODE. Hence there exists infinitely many mutually non-congruent Ricci solitons of this type. Furthermore when c >= 0 and M-n is complete, the Ricci soliton is gradient and in the case it is shrinking, M-n must be the product of the real line and the (n - 1)-sphere. (C) 2012 Elsevier B.V. All rights reserved.