Curvature and Tachibana Numbers

Details Curvature and Tachibana Numbers Curvature and Tachibana Numbers

2009-03-23

arxiv.org/abs/0903.3824v1

Mathematics

Differential Geometry

Scientific paper

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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