CLASSIFICATION OF STEADY GRADIENT RICCI SOLITONS ON TWO-MANIFOLDS

In our very recent published work [Int. J. Geom. Meth. Mod. Phys. 8(4) (2011) 783-796], we considered the Riemannian manifold M = R-2 endowed with the warped metric (g) over bar (x, y) = diag(g(y), 1), where g is a positive function, of C-infinity-class, depending on the variable y only. Within this framework, we found a wide class of 2D gradient Ricci solitons and specialized our results to discuss some case studies. This research is a natural continuation, providing classification results for the subclass of steady gradient Ricci solitons.