On Interpretation of Hyperbolic Angle
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Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.
Abstract
Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.
참고문헌 (7)
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- R. Lopez, "Differential geometry of curves and surfaces in Lorentz-Minkowski space", Int. Electron. J. Geom, 7(1), pp.44~107 (2014)
- E. Nesovic, "On geometric interpretation of pseudo-angle in Minkowski plane", Int. J. Geom. Methods Mod. Phys, 14, pp.12~ (2017)
- E. Nesovic, "Curves in Lorentz spaces", Bollettino U. M. I, 8, pp.685~696 (2005)