Special Killing forms on Lorentzian spin manifolds

The aim of this paper is to give some conformal Killing forms, some Killing and special Killing forms concerning the geometry of Lorentzian spin manifolds admitting imaginary Killing spinors. By the Dirac current flow V φ of an imaginary killing spinor φ. This paper constructs a conformal killing 2-form and a special killing form on lorentzian spin manifold, also gives a way of construction from special killing form of degree p to special killing form p + k(k + 1).