Spinor states on a curved infinite disc with non-zero spin-connection fields

In the paper of Lukman, Mankoc Borstnik, Nielsen (NJP 13 (2011) 103027) one step towards the realistic Kaluza-Klein[like] theories was made by presenting the case of a spinor in $d=(1+5)$ compactified on an (formally) infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless spinor state of a particular charge, coupling the spinor chirally to the corresponding Kaluza-Klein gauge field. The solutions for the massless spinor state were found for a range of spin connection fields, as well as the massive ones for a particular choice of the spin connection field. In this paper we present the massless and massive spinor states for the whole range of parameters of the spin connection field, which allow only one massless solution.