Curvature and Tachibana Numbers

The purpose of this paper is to define the r-th Tachibana number t® of an n-dimentional closed and oriented Riemannian manifold (M,g) as the dimension of the space of all conformal Killing r-forms for r=1,2,…,n-1 and to formulate some properties of these numbers as an analogue to properties of the r-th Betty number b® of a closed and oriented Riemannian manifold.