Naciri, Asmaa2024-09-172024-09-172024-092024-092024-09-06https://hdl.handle.net/11693/115811Cataloged from PDF version of article.Thesis (Master's): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2024.Includes bibliographical references (leave 45-46).We review the basic concepts of space curves, including curvature and torsion. We examine special curves such as Mannheim and Bertrand in a three-dimensional Euclidean space. We define Walker manifolds which are pseudo-Riemannian manifolds with a parallel null distribution. Then we compute Christoffel symbols and Levi-Civita connection components for an arbitrary three-dimensional Walker manifold. Finally, we derive the curvature and torsion of a regular curve on a three-dimensional Walker manifold. Then, we investigate necessary and sufficient conditions for Mannheim curves in a strict three-dimensional Walker manifold. Moreover, we also prove necessary and sufficient conditions of Bertrand curves in a three-dimensional Walker manifold.8, 46 leaves : charts ; 30 cm.Englishinfo:eu-repo/semantics/openAccessWalker manifoldMannheim curvesFrenet frameThesisB162631