  It is shown that on the de Sitter manifolds the tachyonic geodesics are
restricted such that the classical tachyons cannot exist on this manifold at
any time. On the contrary, the theory of the scalar quantum tachyons is free of
any restriction. The tachyonic scalar and Dirac plane waves are deduced in this
geometry, pointing out that these are well-defined, behaving as tempered
distributions at any moment.
