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SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES

Year 2017, Volume: 66 Issue: 2, 276 - 288, 01.08.2017
https://doi.org/10.1501/Commua1_0000000818

Abstract

In this paper, we examine the Lorentzian similar plane curvesusing the hyperbolic structure and spherical arc length parameter. We classifyall self-similar Lorentzian plane curves and give formulas for pseudo shapecurvatures of evolute, involute and parallel curves of a nonnull plane curve

References

  • A. Gray, Modern Diğ erential Geometry of Curves and Surfaces, CRC Press, Boca Raton, A. Saloom and F. Tari, Curves in the Minkowski plane and their contact with pseudo-circles, Geometriae Dedicata (2012), 159:109-124.
  • A. Schwenk-Schellscmidt, U. Simon, M Wiehe, Eigenvalue equations in curve theory Part I: characterization of conic sections, Results in Mathematics, 40, 273-285 (2001).
  • B. B. Mandelbrot, The Fractal Geometry of Nature, New York: W. H. Freeman, 1983.
  • B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.
  • D. Hestenes, New Foundations for Classical Mechanics, Kluwer Academic Publisher, Second Edition, 1999.
  • D. Hestenes, G. Sobczyk, Cliğ ord Algebra to Geometric Calculus: A Uni…ed Language for Mathematics and Physics, Kluwer Academic Publishing, Dordrecht, 1987.
  • F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, P. Zampetti, Geometry of Minkowski Space- time, Springer Briefs in Physics, ISBN: 978-3-642-17977-8 (2011).
  • H.B. Öztekin, M. Ergüt, Eigenvalue equations for Nonnull curve in Minkowski plane, Int. J. Open Probl. Compt. Math. 3, 467–480 (2010).
  • H. Simsek, M. Özdemir, On Conformal Curves in 2-Dimensional de Sitter Space, Adv. Appl. Cliğord Algebras 26, 757–770 (2016).
  • H. Simsek, M. Özdemir, Similar and Self-Similar Curves in Minkowski n-Space, Bull. Korean Math. Soc., 52 , No. 6, pp. 2071-2093 (2015).
  • I. R. Porteous, Cliğ ord Algebras and Classical Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-55177-3 (1995).
  • J. E. Hutchinson, Fractals and Self-Similarity, Indiana University Mathematics Journal, Vol. , N:5, (1981).
  • J. G. Alcázar, C. Hermosoa, G. Muntinghb, Detecting similarity of rational plane curves, Journal of Computational and Applied Mathematics, 269, 1–13 (2014).
  • K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Second Edition, John Wiley & Sons, Ltd., 2003.
  • KS. Chou, C. Qu, Integrable equations arising from motions of plane curves, Pysica D, 162 (2002), 9-33.
  • KS. Chou, C. Qu, Motions of curves in similarity geometries and Burgers-mKdv hierarchies, Chaos, Solitons & Fractals 19 (2004), 47-53.
  • M. Berger: Geometry I. Springer, New York 1998.
  • M. K. Karacan, B. Bükcü, Parallel (Oğ set) Curves in Lorentzian Plane, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24 (1-2), 334- 345 (2008).
  • R. Encheva and G. Georgiev, Curves on the Shape Sphere, Results in Mathematics, 44 (2003), 288.
  • S. Müller, A.Schwenk-Schellscmidt, U. Simon, Eigenvalue equations in curve theory Part II: Evolutes and Involutes, Results in Mathematics, 50, 109-124 (2007).
Year 2017, Volume: 66 Issue: 2, 276 - 288, 01.08.2017
https://doi.org/10.1501/Commua1_0000000818

Abstract

References

  • A. Gray, Modern Diğ erential Geometry of Curves and Surfaces, CRC Press, Boca Raton, A. Saloom and F. Tari, Curves in the Minkowski plane and their contact with pseudo-circles, Geometriae Dedicata (2012), 159:109-124.
  • A. Schwenk-Schellscmidt, U. Simon, M Wiehe, Eigenvalue equations in curve theory Part I: characterization of conic sections, Results in Mathematics, 40, 273-285 (2001).
  • B. B. Mandelbrot, The Fractal Geometry of Nature, New York: W. H. Freeman, 1983.
  • B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Inc., London, 1983.
  • D. Hestenes, New Foundations for Classical Mechanics, Kluwer Academic Publisher, Second Edition, 1999.
  • D. Hestenes, G. Sobczyk, Cliğ ord Algebra to Geometric Calculus: A Uni…ed Language for Mathematics and Physics, Kluwer Academic Publishing, Dordrecht, 1987.
  • F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, P. Zampetti, Geometry of Minkowski Space- time, Springer Briefs in Physics, ISBN: 978-3-642-17977-8 (2011).
  • H.B. Öztekin, M. Ergüt, Eigenvalue equations for Nonnull curve in Minkowski plane, Int. J. Open Probl. Compt. Math. 3, 467–480 (2010).
  • H. Simsek, M. Özdemir, On Conformal Curves in 2-Dimensional de Sitter Space, Adv. Appl. Cliğord Algebras 26, 757–770 (2016).
  • H. Simsek, M. Özdemir, Similar and Self-Similar Curves in Minkowski n-Space, Bull. Korean Math. Soc., 52 , No. 6, pp. 2071-2093 (2015).
  • I. R. Porteous, Cliğ ord Algebras and Classical Groups, Cambridge: Cambridge University Press, ISBN 978-0-521-55177-3 (1995).
  • J. E. Hutchinson, Fractals and Self-Similarity, Indiana University Mathematics Journal, Vol. , N:5, (1981).
  • J. G. Alcázar, C. Hermosoa, G. Muntinghb, Detecting similarity of rational plane curves, Journal of Computational and Applied Mathematics, 269, 1–13 (2014).
  • K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Second Edition, John Wiley & Sons, Ltd., 2003.
  • KS. Chou, C. Qu, Integrable equations arising from motions of plane curves, Pysica D, 162 (2002), 9-33.
  • KS. Chou, C. Qu, Motions of curves in similarity geometries and Burgers-mKdv hierarchies, Chaos, Solitons & Fractals 19 (2004), 47-53.
  • M. Berger: Geometry I. Springer, New York 1998.
  • M. K. Karacan, B. Bükcü, Parallel (Oğ set) Curves in Lorentzian Plane, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24 (1-2), 334- 345 (2008).
  • R. Encheva and G. Georgiev, Curves on the Shape Sphere, Results in Mathematics, 44 (2003), 288.
  • S. Müller, A.Schwenk-Schellscmidt, U. Simon, Eigenvalue equations in curve theory Part II: Evolutes and Involutes, Results in Mathematics, 50, 109-124 (2007).
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Hakan Sımsek This is me

Mustafa Özdemır This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Sımsek, H., & Özdemır, M. (2017). SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 276-288. https://doi.org/10.1501/Commua1_0000000818
AMA Sımsek H, Özdemır M. SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):276-288. doi:10.1501/Commua1_0000000818
Chicago Sımsek, Hakan, and Mustafa Özdemır. “SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 276-88. https://doi.org/10.1501/Commua1_0000000818.
EndNote Sımsek H, Özdemır M (August 1, 2017) SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 276–288.
IEEE H. Sımsek and M. Özdemır, “SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 276–288, 2017, doi: 10.1501/Commua1_0000000818.
ISNAD Sımsek, Hakan - Özdemır, Mustafa. “SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 276-288. https://doi.org/10.1501/Commua1_0000000818.
JAMA Sımsek H, Özdemır M. SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:276–288.
MLA Sımsek, Hakan and Mustafa Özdemır. “SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 276-88, doi:10.1501/Commua1_0000000818.
Vancouver Sımsek H, Özdemır M. SHAPE CURVATURES OF THE LORENTZIAN PLANE CURVES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):276-88.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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