Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 209 - 221, 31.07.2021
https://doi.org/10.33773/jum.937457

Öz

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.

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

Yıl 2021, , 209 - 221, 31.07.2021
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.

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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Arfah Arfah 0000-0002-7654-5520

Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 15 Mayıs 2021
Kabul Tarihi 28 Temmuz 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Arfah, A. (2021). ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE. Journal of Universal Mathematics, 4(2), 209-221. https://doi.org/10.33773/jum.937457
AMA Arfah A. ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE. JUM. Temmuz 2021;4(2):209-221. doi:10.33773/jum.937457
Chicago Arfah, Arfah. “ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE”. Journal of Universal Mathematics 4, sy. 2 (Temmuz 2021): 209-21. https://doi.org/10.33773/jum.937457.
EndNote Arfah A (01 Temmuz 2021) ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE. Journal of Universal Mathematics 4 2 209–221.
IEEE A. Arfah, “ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE”, JUM, c. 4, sy. 2, ss. 209–221, 2021, doi: 10.33773/jum.937457.
ISNAD Arfah, Arfah. “ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE”. Journal of Universal Mathematics 4/2 (Temmuz 2021), 209-221. https://doi.org/10.33773/jum.937457.
JAMA Arfah A. ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE. JUM. 2021;4:209–221.
MLA Arfah, Arfah. “ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE”. Journal of Universal Mathematics, c. 4, sy. 2, 2021, ss. 209-21, doi:10.33773/jum.937457.
Vancouver Arfah A. ON SPHERICAL INDICATRICES AND THEIR SPHERICAL IMAGE OF NULL CURVES IN MINKOWSKI 3-SPACE. JUM. 2021;4(2):209-21.