Vertex angles of simplices in hyperbolic space

This thesis is consists of seven sections. In the first and second sections, the historical knowledges about the studies in hyperbolic space and basic concepts are given, respectively. In the third section, the models of hyperbolic space and the isometries of that models are presented. In the fourth and fifth sections, the n-dimensional sine, n-dimensional polar sine and the relations between them are examined for the Euclidean and spherical simplices, respectively. Moreover, in the fifth section spherical distances to the spherical hyperplane and (n-2)-plane of a point are given. In the sixth section n-dimensional sine, n-dimensional polar sine and relations between them are found for the hyperbolic simplices. Furthermore, hyperbolic distances to the hyperbolic hyperplane and (n-2)-plane of a point are calculated. The seventh section is prepared for the summary of results obtained by that study and its goals. Science Code : 403.02.01 Key Words : Hyperbolic space, simplex, n-hedral angle, n-dimensional sine