Pseudo quaternions, pseudo hyperbolic space pseudo spherical space

This thesis consist of fourth section. In the first section, after giving the short historical knowledge, in the second section, the properties of quaterenionic product and the algebraic structure of quaternions are introduced. In the third section, the 3 and 4-dimensional rotations are given by using the quaternionic product. Moreover, the spherical sine and spherical cosine rule are presented. In the last section, we give pseudo quaternionic product with n-index. Afterwards, by using this definition ,the semi-quaternionic algebra is studied in the case n=0,1.