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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k096/k09614h.htm

Last modified: October 13, 2010