Harmonic and biharmonic Riemannain submersions from Sol space

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