The conformal transformation group of a compact homogeneous Riemannian manifold

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

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 =...

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 Manifolds Covered by a Riemannian Homogeneous Manifold

A Bound for the Dimension of the Automorphism Group of a Homogeneous Compact Complex Manifold

Let X be a homogeneous compact complex manifold, and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. Examples show that dim Aut(X) can grow exponentially in n = dimX. In this note it is shown that dim Aut(X) ≤ n − 1 + (2n− 1 n− 1 ) when n ≥ 3. Thus, dim Aut(X) is at most exponential in n. The proof relies on an upper bound for the dimension of the space of sections of the...