Dual quaternions and dual projective spaces

In this study, dual unitary matrices SU(D)(2) were obtained. We correspond to one to one elements of the unit dual sphere S(D)(3) 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)) congruent to S(3)/{+/- 1} = RP(3) known as the real projective spaces was generalized to the dual projective space and then, the equality SO(D(3)) congruent to S(D)(3)/{+/- 1} = DP(3) was acquired. In particular, 2-sphere S(2) was obtained by considering dual parts as zero or S(D)(3). Hence, it was found that Hop fibrilation map of S(2) call be used for Twistors in quantum mechanics applications. (C) 2007 Elsevier Ltd. All rights reserved.