Recently we have constructed the conformal gravity with metric and torsion,View original: http://arxiv.org/abs/1101.2566
finding the gravitational field equations that give the conservation laws and
trace condition; in the present paper we apply this theory to the case of ELKO
matter field, proving that their spin and energy densities once the matter
field equations are considered imply the validity of the conservation laws and
trace condition mentioned above.