Dual quaternions and dual projective spaces

Abstract: In this study, dual unitary matrices SU D(2) were obtained. We correspond to one to one elements of the unit dual sphere with the dual unitary matrices SU D(2). Thus, we express spherical concepts such as meridians of longitude and parallels of latitude on SU D(2). The equality SO(R 3)≅ S 3/{±1}= RP 3 known as the real projective spaces was generalized to the dual projective space and then, the equality was acquired. In particular, 2-sphere S 2 was obtained by considering dual parts as zero of . Hence, it was found that Hop fibriation map of S 2 can be used for Twistors in quantum mechanics applications. [Copyright &y& Elsevier]