Research Article
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Year 2022, Volume: 71 Issue: 1, 79 - 94, 30.03.2022
https://doi.org/10.31801/cfsuasmas.865100

Abstract

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İlginiz ve alakanız için çok teşekkür ederim.

References

  • Ates, F., Kaya, S., Yaylı, Y., Ekmekci, F. N., Generalized similar Frenet curves, Mathematical Sciences and Applications E-notes, 5(2) (2017), 26-35. https://doi.org/10.36753/mathenot.421731
  • Bejancu, A., Lightlike curves in Lorentz manifolds, Publ. Math. Debrecen, 44(1–2) (1994), 145–155.
  • Berger, M., Geometry I, Springer, New York, 1998.
  • Bonnor, W. B., Null curves in a Minkowski space-time, Tensor N.S., 20 (1969), 229–242.
  • Brook, A., Bruckstein, A. M., Kimmel, R., On Similarity-Invariant Fairness Measures. In: Kimmel, R., Sochen, N. A., Weickert, J., (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space, Lecture Notes in Computer Science, 3459, Springer, Berlin, Heidelberg, 2005. https://doi.org/10.1007/11408031 39
  • Budinich, P., Null vectors, spinors, and strings, Comm. Math. Phys., 107(3) (1986), 455-465.
  • Camci, Ç, İlarslan, K., Sucurovic, E., On pseudohyperbolical curves in Minkowski Spacetime, Turk. J. Math., 27(2) (2003), 315–328.
  • Chou, K. S., Qu, C., Integrable equations arising from motions of plane curves, Proceedings of Institute of Mathematics of NAS of Ukraine, 43(1) (2002), 281–290.
  • Chou, K. S., Qu, C., Motions of curves in similarity geometries and Burgers-mKdV hierarchies,Chaos, Solitons & Fractals, 19 (2004), 47-53. https://doi.org/10.1016/S0960-(03)00060-2
  • Cöken, A. C., Ciftci, Ü., On the Cartan curvatures of a null curve in Minkowski space-time, Geom. Dedicata, 114 (2005), 71-78. https://doi.org/10.1007/s10711-005-4804-1
  • Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, volume 364 of Mathematics and Its Aplications. Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1996.
  • Encheva, R., Georgiev, G., Curves on the shape sphere, Results in Mathematics, 44 (2003), 279-288.
  • Encheva, R., Georgiev, G., Similar Frenet curves, Results in Mathematics, 55(3-4) (2009), 359–372. https://doi.org/10.1007/s00025-009-0407-8
  • Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, Second Edition, John Wiley & Sons, Ltd., 2003.
  • Ferrandez, A., Gimenez, A., Lucas, P., Null helices in Lorentzian space forms, Int. J. Mod. Phys. A, 16 (2001), 4845-4863. Doi: 10.1142/S0217751X01005821
  • Ferrandez, A., Gimenez, A., Lucas, P., Geometrical particle models on 3D null curves, Phys. Lett. B, 543(3-4) (2002), 311–317. Doi: 10.1016/S0370-2693(02)02450-4
  • Grigorchuk, R., Sunic, Z., Self Similarity an Branching Group Theory, Groups St Andrews, London Mathematical Society Lecture Note Series: 339(1), 2005.
  • Gürses, M., Motion of curves on two-dimensional surfaces and soliton equations, Physics Letters A, 241(6) (1998), 329-334. https://doi.org/10.1016/S0375-9601(98)00151-0
  • Hughston, L.P., Shaw, W.T., Real classical strings, Proc. Roy. Soc. London Ser. A, 414 (1987), 415-422.
  • Hughston, L.P., Shaw, W.T., Classical strings in ten dimensions, Proc. Roy. Soc. London Ser. A, 414 (1987), 423-431.
  • Hutchinson, J.E., Fractals and self-similarity, Indiana University Mathematics Journal, 30(5) (1981).
  • Kamishima, Y., Lorentzian similarity manifolds, Cent. Eur. J. Math., 10(5) (2012), 1771-1788. Doi: 10.2478/s11533-012-0076-9
  • Li, S.Z., Invariant Representation, Matching and Pose Estimation of 3D Space Curves Under Similarity Transformation, Pattern Recognition, 30(3) (1997), 447-458. https://doi.org/10.1016/S0031-3203(96)00089-1
  • Nersessian, A., Ramos, E., Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123–128. https://doi.org/10.1016/S0370-2693(98)01408-7
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., London, 1983.
  • Sahbi, H., Kernel PCA for similarity invariant shape recognition, Neurocomputing, 70 (2007), 3034-3045. https://doi.org/10.1016/j.neucom.2006.06.007
  • Şimşek, H., Özdemir, M., Similar and self-similar curves in Minkowski n-space, Bull. Korean Math. Soc. 52(6) (2015), 2071-2093. https://doi.org/10.4134/BKMS.2015.52.6.2071

Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces

Year 2022, Volume: 71 Issue: 1, 79 - 94, 30.03.2022
https://doi.org/10.31801/cfsuasmas.865100

Abstract

In this paper, differential invariants of null Cartan curves are studied in (n+2) dimensional Lorentzian similarity geometry. The fundamental theorem for a null Cartan curve in similarity geometry is investigated and the characterization of all self-similar null Cartan curves parameterized by de Sitter parameter in Minkowski space-time is given.

References

  • Ates, F., Kaya, S., Yaylı, Y., Ekmekci, F. N., Generalized similar Frenet curves, Mathematical Sciences and Applications E-notes, 5(2) (2017), 26-35. https://doi.org/10.36753/mathenot.421731
  • Bejancu, A., Lightlike curves in Lorentz manifolds, Publ. Math. Debrecen, 44(1–2) (1994), 145–155.
  • Berger, M., Geometry I, Springer, New York, 1998.
  • Bonnor, W. B., Null curves in a Minkowski space-time, Tensor N.S., 20 (1969), 229–242.
  • Brook, A., Bruckstein, A. M., Kimmel, R., On Similarity-Invariant Fairness Measures. In: Kimmel, R., Sochen, N. A., Weickert, J., (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space, Lecture Notes in Computer Science, 3459, Springer, Berlin, Heidelberg, 2005. https://doi.org/10.1007/11408031 39
  • Budinich, P., Null vectors, spinors, and strings, Comm. Math. Phys., 107(3) (1986), 455-465.
  • Camci, Ç, İlarslan, K., Sucurovic, E., On pseudohyperbolical curves in Minkowski Spacetime, Turk. J. Math., 27(2) (2003), 315–328.
  • Chou, K. S., Qu, C., Integrable equations arising from motions of plane curves, Proceedings of Institute of Mathematics of NAS of Ukraine, 43(1) (2002), 281–290.
  • Chou, K. S., Qu, C., Motions of curves in similarity geometries and Burgers-mKdV hierarchies,Chaos, Solitons & Fractals, 19 (2004), 47-53. https://doi.org/10.1016/S0960-(03)00060-2
  • Cöken, A. C., Ciftci, Ü., On the Cartan curvatures of a null curve in Minkowski space-time, Geom. Dedicata, 114 (2005), 71-78. https://doi.org/10.1007/s10711-005-4804-1
  • Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, volume 364 of Mathematics and Its Aplications. Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1996.
  • Encheva, R., Georgiev, G., Curves on the shape sphere, Results in Mathematics, 44 (2003), 279-288.
  • Encheva, R., Georgiev, G., Similar Frenet curves, Results in Mathematics, 55(3-4) (2009), 359–372. https://doi.org/10.1007/s00025-009-0407-8
  • Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, Second Edition, John Wiley & Sons, Ltd., 2003.
  • Ferrandez, A., Gimenez, A., Lucas, P., Null helices in Lorentzian space forms, Int. J. Mod. Phys. A, 16 (2001), 4845-4863. Doi: 10.1142/S0217751X01005821
  • Ferrandez, A., Gimenez, A., Lucas, P., Geometrical particle models on 3D null curves, Phys. Lett. B, 543(3-4) (2002), 311–317. Doi: 10.1016/S0370-2693(02)02450-4
  • Grigorchuk, R., Sunic, Z., Self Similarity an Branching Group Theory, Groups St Andrews, London Mathematical Society Lecture Note Series: 339(1), 2005.
  • Gürses, M., Motion of curves on two-dimensional surfaces and soliton equations, Physics Letters A, 241(6) (1998), 329-334. https://doi.org/10.1016/S0375-9601(98)00151-0
  • Hughston, L.P., Shaw, W.T., Real classical strings, Proc. Roy. Soc. London Ser. A, 414 (1987), 415-422.
  • Hughston, L.P., Shaw, W.T., Classical strings in ten dimensions, Proc. Roy. Soc. London Ser. A, 414 (1987), 423-431.
  • Hutchinson, J.E., Fractals and self-similarity, Indiana University Mathematics Journal, 30(5) (1981).
  • Kamishima, Y., Lorentzian similarity manifolds, Cent. Eur. J. Math., 10(5) (2012), 1771-1788. Doi: 10.2478/s11533-012-0076-9
  • Li, S.Z., Invariant Representation, Matching and Pose Estimation of 3D Space Curves Under Similarity Transformation, Pattern Recognition, 30(3) (1997), 447-458. https://doi.org/10.1016/S0031-3203(96)00089-1
  • Nersessian, A., Ramos, E., Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123–128. https://doi.org/10.1016/S0370-2693(98)01408-7
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., London, 1983.
  • Sahbi, H., Kernel PCA for similarity invariant shape recognition, Neurocomputing, 70 (2007), 3034-3045. https://doi.org/10.1016/j.neucom.2006.06.007
  • Şimşek, H., Özdemir, M., Similar and self-similar curves in Minkowski n-space, Bull. Korean Math. Soc. 52(6) (2015), 2071-2093. https://doi.org/10.4134/BKMS.2015.52.6.2071
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hakan Şimşek 0000-0002-1028-2676

Publication Date March 30, 2022
Submission Date January 20, 2021
Acceptance Date August 5, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

APA Şimşek, H. (2022). Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 79-94. https://doi.org/10.31801/cfsuasmas.865100
AMA Şimşek H. Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):79-94. doi:10.31801/cfsuasmas.865100
Chicago Şimşek, Hakan. “Similar and Self-Similar Null Cartan Curves in Minkowski-Lorentzian Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 79-94. https://doi.org/10.31801/cfsuasmas.865100.
EndNote Şimşek H (March 1, 2022) Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 79–94.
IEEE H. Şimşek, “Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 79–94, 2022, doi: 10.31801/cfsuasmas.865100.
ISNAD Şimşek, Hakan. “Similar and Self-Similar Null Cartan Curves in Minkowski-Lorentzian Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 79-94. https://doi.org/10.31801/cfsuasmas.865100.
JAMA Şimşek H. Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:79–94.
MLA Şimşek, Hakan. “Similar and Self-Similar Null Cartan Curves in Minkowski-Lorentzian Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 79-94, doi:10.31801/cfsuasmas.865100.
Vancouver Şimşek H. Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):79-94.

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

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