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Curvature and Tachibana Numbers

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Preprint
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arXiv
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Abstract

The purpose of this paper is to define the r-th Tachibana number t(r) of an n-dimentional 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 analogue to properties of the r-th Betty number b(r) of a closed and oriented Riemannian manifold.

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