No abstract

Abstract. In this paper, when N is a compact Riemannian manifold of class (A), we consider the existence of some warping functions on Riemannian warped product manifolds M = [a, ∞) × f N with prescribed scalar curvatures.

Abstract. In this paper, we prove the existence and the nonexistence of warping functions on Riemannian warped product manifolds with some prescribed scalar curvatures according to the fiber manifolds of class (A).

In this paper, we consider Ricci curvature of conformal deformation on compact 2-manifolds. And we prove that, by the conformal deformation, the resulting manifold is an Einstein manifold.

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on Riemannian warped product manifold M = (a, ∞)× f N with prescribed scalar curvature functions.