RELATIONS BETWEEN AREAS OF LORENTZIAN SPHERICAL REGIONS

Year 2020, Volume: 2 Issue: 1, 1 - 8, 04.03.2020

Gülay Koru Yücekaya

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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