FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 6, PAGES 211-222

Curvature and Tachibana Numbers

S. E. Stepanov

Abstract

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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 $r\; =\; 1,\; 2,$¼, 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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Last modified: October 13, 2010