Curvature and Tachibana numbers

The purpose of this paper is to define the $r$th Tachibana number $t_r$ of an $n$-dimensional closed and oriented Riemannian manifold $(M,g)$ as the dimension of the space of all conformal Killing $r$-forms for $r=1,2,\dots,n-1$ and to formulate some properties of these numbers as an analogue to properties of the $r$th Betti number $b_r$ of a closed and oriented Riemannian manifold.