ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE

Yıl 2021, Cilt: 4 Sayı: 2, 209 - 221, 31.07.2021

Arfah Arfah

https://doi.org/10.33773/jum.937457

Öz

In this paper, we investigate the spherical images of null curves and null helixes in Minkowski 3-space. We provide the spherical indicatrices of null curves in Minkowski 3-space with their causal characteristics. We also show the conditions of spherical indicatrices of null curves to be a curve lying on pseudo-sphere in Minkowski 3-space. In addition, we give the properties of spherical indicatrices of null curves satisfying generalized helices and lying on pseudo-sphere in Minkowski 3-space.

Anahtar Kelimeler

Null curves, Null Helices, Spherical Indicatrices, Minkowski Space

Kaynakça

• A.T. Ali, New spherical curves and their spherical indicatrices, Global Journal of Advance Research on Classical and Modern Geometries, 2(1) (2009),28--38.
• M. M. Lipschutz, Schaum’s Outline of Differential Geometry, McGraw-Hill, Canada (1969).
• R. Lopez, Differential geometry of curves and surface in Lorentz-Minkowski space, International electronic journal of geometry, 1(2) (2014), 44-107.
• H. K. Mohajan, Minkowski geometry and space-time manifold in relativity, Journal of Environmental Techniques, 1 (2013), 101--109.
• B. O’neil, Semi-Riemannian Geometry and Its Application to Relativity, Academic press, New York (1983).
• H.K. Samanci, O. Kalkan, S. Celik ,The timelike bezier spline in Minkowski 3-space, Journal of science and arts, Vol: 2 (2019), 357 – 374.
• J. Inoguchi and S. Lee, Null curves in Minkowski 3-space, International Electronic Journal of Geometry, 1(2) (2008), 40--83.
• K.L. Duggal and D.H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World scientific, Singapore (2007).
• A. Ferrandez, A. Gimenez and P. Lucas, Null generalized helices in Lorentz-Minkowski spaces, Journal of Physics A: Mathematical and General, 35 (2002), 8243--8251.
• L. P. Hungston and W.T. Shaw, Real classical strings, Proc. Roy. Soc. London Ser. A, (1987), 415–422.
• A. Nersian and E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B., 445 (1998), 123--128.
• W. Kuhnel, Differential Geometry: Curves - Surfaces - Manifolds, American Mathematical Societies, Rhode Island (1999).
• M. P. D. Carmo, Differential Geometry of Curves and Surfaces, Dover Publication Inc., New York (2016).
• J. Philips, Freedom in Machinery, Cambridge University Press, New York (1990).
• Chung, S.K., A study on spherical indicatrix of space curve in $\mathbf{E}^3$, Journal of Mathematical Education, XX(3) (1982), 23–26.
• M. Bilici, M. and A. Ali, On the natural lift curves for the involute spherical indicatrices in Minkowski 3- space, Malaya Journal of Mathematics, 5(12) (2017), 407-–415.
• E. V. Shinkin, Handbook and Atlas of Curves, CRC Press, Florida (1995).
• J. Qian and Y. H. Kim, Directional associated curves of a null curve in Minkowski 3-space, Bull. Korean Math. Soc. 52(1) (2015), 183-–200
• U. Ozturk, E. B. K. Ozturk and K. Ilarslan, On the Involute-Evolute of the Pseudonull Curve in Minkowski 3-Space, Journal of Applied Mathematics 2013 (2013), 5--8.
• J. Qian, J. Liu, X. Tian and Y. H. Kim, Structure functions of pseudo null curves in Minkowski 3-space, Mathematics 8 (75) (2020), 1--15.
• K. Fatma and Y. Yayli, The Fermi-Walker derivative on the spherical indicatrix of spacelike curve in Minkowski 3-space, Adv. Appl. Clifford Algebras 26 (2016), 625–644.