Characterizations of space curves according to bishop darboux vector in euclidean 3-space

In this thesis we obtained some characterizations of space curves according to Bihop frame in Euclidean 3-space by using Laplacian operator and Levi-Civita connection. In the first section, the abstract about the subject is given. In the second section, basic definitions are given. In the third section, some part about Bishop Frame which is base of our research from [19] are given. In the fourth section, some parts from referance [25] are given. In the fifth section, we obtain some chracterization of space curves according to Bishop Frame in 3-Eucledian Space by using Laplace oparator and Levi-Civita connection. In the sixth section, harmonic 1-type T ⃗,N ⃗_1,N ⃗_2 curves are studied. Furthermore some characterizations about biharmonic T ⃗,N ⃗_1,N ⃗_2 curves are obtained.