DOI: 10.18586/msufbd.1929487 ISSN: 2147-7930

A Geometric Investigation of Multiplicative One-Parameter Motions in Lorentzian Geometry

Hasan Es
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The trigonometric framework of the multiplicative Lorentzian plane, together with the notions of multiplicative rotations and motions, has been investigated in earlier studies. In this paper, parameterized motions defined on the multiplicative Lorentzian plane are examined. By employing multiplicative calculus, the fundamental properties of these motions are analyzed, and the velocity components, velocity law, and relationships among velocities are derived. Furthermore, acceleration quantities and their corresponding relations are obtained. To provide a geometric description of motion, moving coordinate systems are adapted to the multiplicative Lorentzian setting. In this context, the differential equations of the multiplicative Lorentzian moving frame are established, and the associated multiplicative Pfaffian forms are introduced. Moreover, a third multiplicative Lorentzian plane is defined, and the relative motions among the three planes are investigated. The results contribute to the development of multiplicative Lorentzian kinematics and provide a basis for future studies.

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