Curvature and Tachibana numbers

S. E. Stepanov

Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 211-222.

Résumé

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.

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