  We present definitions and properties of conformal Killing, Killing and
planarity forms on a Riemannian manifold and determine Tachibana, Killing and
planarity numbers as an analog of the well known Betti numbers. We state some
set of conditions to characterize these numbers. Moreover, we formulate the
main results on the relationship between the Betti, Tachibana, Killing and
planarity numbers.
