The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations

Conformal vector fields and conformal transformations on a Riemannian manifold

In this paper first it is proved that if ξ is a nontrivial closed conformal vector field on an n-dimensional compact Riemannian manifold (M, g) with constant scalar curvature S satisfying S ≤ λ1(n − 1), λ1 being first nonzero eigenvalue of the Laplacian operator ∆ on M and Ricci curvature in direction of a certain vector field is non-negative, then M is isometric to the n-sphere S(c), where S =...

Conformal Deformation of a Riemannian Metric to Constant Scalar Curvature

A well-known open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe's paper claimed to solve the problem in the affirmative, it was found by N. Trudinger [6] in 1968 tha...

Curvature Structures and Conformal Transformations

1. The notion of a "curvature structure" was introduced in §8, Chapter 1 of [ l ] . In this note we shall consider some of its applications. The details will be presented elsewhere. Let (M, g) be a Riemann manifold. Whenever convenient, we shall denote the inner product defined by g, by ( ). DEFINITION. A curvature structure on (M, g) is a (1, 3) tensor field T such that, for any vector fields ...

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold