In this paper, we study to express the theory of curves including a wide section of Lorentzian geometry in terms of spinors with two hyperbolic components which has an important place in the Clifford algebra. In other words, we express the rotation, element of SO(1, 3), between the Frenet frame and the other frame defined as alternatively of the (spacelike or timelike) curves in Minkowski space R 3 1 in terms of the rotation, element of SU (2, H), with the aid of the hyperbolic spinors.Mathematics Subject Classification. 62J05, 62J07.

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In this paper, we have obtained spinor with two complex components representations of Involute Evolute curves in E 3. Firstly, we have given the spinor equations of Frenet vectors of two curves which are parameterized by arc-length and have an arbitrary parameter. Moreover, we have chosen that these curves are Involute Evolute curves and have matched these curves with different spinors. Then, we have investigated the answer of question "How are the relationships between the spinors corresponding to the Involute Evolute curves in E 3 ?". Finally, we have given an example which crosscheck to theorems throughout this study.

The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and n2 of the curve, [1]. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifying curves in R 3 1 . Moreover, by the aid of these characterizations, we have investigated semi real quaternionic rectifying curves in semiquaternionic space Qv.

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Spinors are used in physics quite extensively. Basically, the forms of use include Dirac four-spinors, Pauli three-spinors and quaternions. Quaternions in mathematics are essentially equivalent to Pauli spin matrices which can be generated by regarding a quaternion matrix as compound. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined Fibonacci spinors using the Fibonacci quaternions. Later, we have established the structure of algebra for these spinors. Finally, we have proved some important formulas such as Binet and Cassini formulas which are given for some series of numbers in mathematics for Fibonacci spinors.

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