Harmonic and biharmonic Riemannain submersions from Sol space

In this paper, we give a complete classifification of harmonic and biharmon<br />ic Riemannian submersions &pi; : (R^3 , g_Sol) &rarr; (N^2 , h) from Sol space into a<br />surface by proving that there is neither harmonic nor biharmonic Riemann<br />ian submersion &pi; : (R^3 , g_Sol) &rarr; (N^2 , h) from Sol space no matter what<br />the base space (N2 , h) is. We also prove that a Riemannian submersion<br />&pi; : (R^3 , g_Sol) &rarr; (N^2 , h) from Sol space exists only when the base space is<br />a hyperbolic space form.