Abstract
We consider the problem of deforming a metric in its conformal class on a closed manifold, such that the k-curvature defined by the Bakry-Emery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-Emery Ricci tensor belongs to a negative cone. Moveover, the Monge-Amp`ere type equation with respect to the Bakry-Emery Ricci tensor is also considered.
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