# Prescribing curvature problem of Bakry-Émery Ricci tensor

Research paper by LiXia Yuan

Indexed on: 22 Mar '13Published on: 22 Mar '13Published in: Science China Mathematics

#### 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-Émery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-Émery Ricci tensor belongs to a negative cone. Moveover, the Monge-Amp`ere type equation with respect to the Bakry-Émery Ricci tensor is also considered.