A class of fully nonlinear equations on the closed manifold

作者：Lu, Weina; Zhang, Xiaoling^*; Yang, Jinhua

来源：Differential Geometry and its Applications, 2018, 61: 9-19.

DOI：10.1016/j.difgeo.2018.08.001

• k-order elementary symmetric function
• Prescribed curvature problem

A generalized k-Yamabe problem is considered in this paper. Denoting Ric and R the Ricci tensor and the scalar curvature of a Riemannian space (M,g) respectively, we consider the sigma(k)-type equation sigma(k)(lambda(st)) = const., where lambda(st) are the eigenvalues of the symmetric tensor sRic - tR.g and at is the k-th elementary symmetric polynomial. We show that the equation is solvable in a conformal class if sRic - tR.g is in the convex cone Gamma k(+) and 2t > s > 0.

• 出版日期2018-12
• 单位新疆师范大学; 新疆大学