Geodesic
Curvature and Tachibana numbers
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 211-222

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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. 
@article{FPM_2009_15_6_a13,
     author = {S. E. Stepanov},
     title = {Curvature and {Tachibana} numbers},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {211--222},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a13/}
}
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S. E. Stepanov. Curvature and Tachibana numbers. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 6, pp. 211-222. http://geodesic.mathdoc.fr/item/FPM_2009_15_6_a13/