- Hagia Sophia Journal of Geometry
- Vol: 2 Issue: 1
- RELATIONS BETWEEN AREAS OF LORENTZIAN SPHERICAL REGIONS
RELATIONS BETWEEN AREAS OF LORENTZIAN SPHERICAL REGIONS
Authors : Gülay Koru Yücekaya
Pages : 1-8
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Publication Date : 2020-03-04
Article Type : Other
Abstract :In this study, during the one-parameter closed spherical motion in 3-dimensional Lorentzian space , the unit time-like Steiner vector of the motion; the end points of the orthonormal triad of the K moving Lorentzian sphere, where are the space-like vectors and is the time-like vector, are expressed in terms of field vectors of the regions that are limited by the spherical orbits on the fixed unit Lorentzian sphere during the one-parameter closed spherical motion . Furthermore, for one-parameter closed spherical motion , relations and results between the areas obtained by field vector, of the spherical region bounded by the closed spherical space-like curve (X) drawn by a fixed point X, which selected from the moving Lorentzian sphere on the fixed unit Lorentzian sphere K and in a closed spherical motion ; the orthonormal vectors , which selected in the moving unit Lorentzian sphere K, the spherical regions of the end points on the sphere that the spherical orbits of the fixed unit Lorentzian sphere are constrained. In addition, the correlations and results obtained were analyzed using the new expression of the unit time-like Steiner vector of the motion and the same results were obtained.Keywords : One-parameter closed Lorentzian spherical motion, Lorentzian spherical curve, time-like vector, time-like Steiner vector, Area of a Lorentzian spherical region