The schlafli differential formula in semi-Euclidian space

Ill SCBDLAFLI DIFFERENTIAL FORMULA IN SEMI-EUCLIDIAN SPACE (M.Sc. Thesis) Murat SAVAŞ GAZI UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY August 2004 ABSTRACT This thesis is consists of eight chapters. In chapter 1, we have given some information about history of Schlafli differential formula. In chapter 2, given basic definitions, concepts and properties are given. In chapter 3, the definition of a hyperquadrics, the classification of hyperquadrics and the isometries of two hyperquadrics are given. Morever, in that chapter n-simplex and its faces on a hyperquadrics are defined. In chapter 4, the coordinate maps are examined with respect to the causalcharacter of a vector for the volume element and the proof of Schlafli's differential formula given by Kneser in semi-Euclidian space. In chapter 5, the generalization of Schlafli's differential formula to the simplices on the unit hyperquadric is given. In chapter 6, Santalo's formula in three dimensions is proved by giving the definitions of polar dual and complementary dual of a simplices in arbitrary dimensions. In chapter 7, some results with related to dihedral angle at these faces with odd and even dimensions are given, by using the generalization of Gauss-Bonnet and Santalo's formula for the volume of simplices. In chapter 8, the summary of the results obtained from that study and its targets are given.IV Science Code : 403.02.01 Key Words : Simplex, Volume, Schlafli Page Number: 84 Adviser : Prof. Dr. Baki KARLI?A