CURVATURE AND TACHIBANA NUMBERS

摘要

The purpose of this paper is to define the rth 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,..., n - 1 and to formulate some properties of these numbers as an analog of properties of the rth Betti number b_r of a closed and oriented Riemannian manifold.