A class of fully nonlinear equations on the closed manifold

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 σk-type equation σk(λst)=const., where λst are the eigenvalues of the symmetric tensor sRic−tR⋅g and σk 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 Γk+ and 2t>s>0.