Constant angle surfaces in non-Euclidean spaces

This study consists offive sections. In the first section, the basic definitions of Euclidean space was given. In the second part, the most important definitions and theorems of Lorentz space were given. In the third section, fixed-angle surfaces in 3-dimensional Euclidean space have been examined. In the fourth section, a characterization of constant angle surfaces for Euclidean 3-space was investigated. In the first part of the fifth section, timelike constant angle surfaces with fixed spacelike direction were examined. In the second part of the fifth section, spacelike constant surfaces with fixed spacelike direction were examined. Keywords: Constant angle surfaces, Euclidean space, Lorentzian space