Prescribing curvature problem of Bakry-mery Ricci tensor

作     者：YUAN LiXia 

作者机构：Department of MathematicsZhejiang University Department of MathematicsXinjiang Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第9期

页      面：1935-1944页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Bakry-émery Ricci tensor k-curvature 

摘      要：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-mery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-mery Ricci tensor belongs to a negative cone. Moveover, the Monge-Ampère type equation with respect to the Bakry-mery Ricci tensor is also considered.