Dual quaternions and dual projective spaces

In this study, dual unitary matrices SUD(2) were obtained. We correspond to one to one elements of the unit dual sphere SD3 with the dual unitary matrices SUD(2). Thus, we express spherical concepts such as meridians of longitude and parallels of latitude on SUD(2).The equality SO(R3) ≅ S3/{±1} = RP3 known as the real projective spaces was generalized to the dual projective space and then, the equality SO(D3)≅SD3/{±1}=DP3 was acquired.In particular, 2-sphere S2 was obtained by considering dual parts as zero of SD3. Hence, it was found that Hop fibriation map of S2 can be used for Twistors in quantum mechanics applications.