BACK TO TACHIBANA NUMBERS OF RIEMANNIAN MANIFOLDS

Abstract

The Tachibana number $t_p (M)$ of a closed $n$-dimensional Riemannian manifold $(M,g)$ is defined as the dimension of the vector space of conformally Killing $p$-forms, for $1\leq p\leq n-1$, on $(M,g)$. In this paper, we will prove vanishing and estimate propositions for Tachibana numbers $t_p (M)$ of closed $n$-dimensional Riemannian manifolds, serving as analogues to the vanishing and estimate theorems for their Betti numbers $b_p (M)$.