Liouville and geodesic Ricci solitons
A Riemannian manifold \((M, g)\) carries a Ricci soliton if \[ L_V g + 2 S_g + 2 \lambda g = 0, \] where \(S_g\) is its Ricci tensor, \(L_V\) is the Lie derivative operator with respect a vector field \(V\) and \(\lambda\) is a real scalar. The Ricci soliton is shrinking, steady or expanding according as \(\lambda\) is negative, zero or positive respectively. In this paper, the authors have proved that if \(M\) is Ricci flat then its tangent bundle carries a \(1\)-parameter family of shrinking Liouville Ricci solitons and if \(M\) is flat then its tangent bundle carries a steady geodesic Ricci soliton.
scientific article; zbMATH DE number 5638300
scientific article