Conformal connections and conformal transformations

2.1.1 Conformal Transformations......................... 6

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 =...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

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 ...

Conformal connections on Lyra manifolds

We give an algebraic characterization of the case when conformal Weyl and conformal Lyra connections have the same curvature tensor. It is determined a (1,3)-tensor field invariant to certain transformation of semi-symmetric connections, compatible with Weyl structures on conformal manifolds. It is studied the case when this tensor is vanishing. M.S.C. 2000: 53B05, 53B20, 53B21.