RIEMANNIAN SUBMERSIONS FROM RIEMANN SOLITONS

In the present paper, we study a Riemannian submersion pi from a Riemann soliton (M1, g,xi, lambda) onto a Riemannian manifold (M2, g ' ). We first calculate the sectional curvatures of any fibre of pi and the base manifold M2. Using them, we give some necessary and sufficient conditions for which the Riemann soliton (M1, g, xi, lambda) is shrinking, steady or expanding. Also, we deal with the potential field xi of such a Riemann soliton is conformal and obtain some characterizations about the extrinsic vertical and horizontal sectional curvatures of pi.