This article is cited in 20 papers

Curvature and Tachibana numbers

S. E. Stepanov

Finance Academy under the Government of the Russian Federation

Abstract: The aim of this paper is to define the $r$th Tachibana number $t_r$ of an $n$-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing $r$-forms, for $r=1,2,\dots,n-1$. We also describe properties of these numbers, by analogy with properties of the Betti numbers $b_r$ of a compact oriented Riemannian manifold.
Bibliography: 25 titles.

Keywords: compact Riemannian manifold, differential forms, elliptic operator, scalar invariants.

UDC: 514.762.212

MSC: 53C21, 58A10

Received: 13.03.2010 and 12.12.2010

DOI: 10.4213/sm7711

 English version: Sbornik: Mathematics, 2011, 202:7, 1059–1069

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