RELATIONS BETWEEN AREAS OF LORENTZIAN SPHERICAL REGIONS

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

References

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