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R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları

Year 2018, Volume: 22 Issue: 3, 1007 - 1014, 01.06.2018

Uğur Gözütok Yasemin Sağıroğlu

https://doi.org/10.16984/saufenbilder.341517

Abstract

 Bu çalışmada  tane eğrinin üreteç diferansiyel invaryantları
belirlenmiş olup, bu üreteç kümesinin fonksiyonel bağımsız olduğu
gösterilmiştir. Ayrıca bu diferansiyel invaryantlar kullanılarak  de iki tane li
eğri ailesinin denklik problemi araştırılmıştır.

Keywords

afin diferansiyel geometri invaryant eğriler

References

  • R.G. Aripov, D. Khadjiev, The Complete system of global differential and integral invariants of a curve in Euclidean geometry, Russian Mathematics, vol. 51, no. 7, pp. 1-14, 2007.
  • W. Blaschke, Affine Differentialgeometrie, Springer, Berlin, 1923.
  • R.B. Gardner, G.R. Wilkens, The fundamental theorems of curves and hypersurfaces in centro-affine geometry, Bull. Belg. Math. Soc., vol. 4, pp. 379-401, 1997.
  • S. Izumiya, T. Sano, Generic afine differential geometry of space curves, Proceedings of the Royal Society of Edinburg, vol. 128, no. A, pp. 301-314, 1998.
  • D. Khadjiev, The Application of Invariant Theory to Differential Geometry of Curves. Fan Publ, Tashkent, 1988.
  • D. Khadjiev, Ö. Pekşen, The Complete system of global differential and integral invariants for equi-affine curves, Differential Geom. Appl., vol. 20, pp. 167-175, 2004.
  • H. Liu, Curves in affine and semi-Euclidean Spaces, Result. Math., vol. 65, pp. 235-249, 2014.
  • Y. Sağıroğlu, Affine Differential Invariants of Curves: The Equivalence of Parametric Curves in Terms of Invariants. LAP LAMBERT Academic Publishing, 2012.
  • Y. Sağıroğlu, The Equivalence problem for parametric curves in one-dimensional affine space, Int. Math. Forum, vol. 6, no. 4, pp. 177-184, 2011.
  • P.A. Schirokow, A.P. Schirokow, Affine Differentialgeometrie, Teubner, Leipzig, 1962.
  • B. Su, Affine Differential Geometry, Science Press, Beijing, 1983.

Affine Differential Invariants of a Family of n Curves in R^2

Year 2018, Volume: 22 Issue: 3, 1007 - 1014, 01.06.2018

Uğur Gözütok Yasemin Sağıroğlu

https://doi.org/10.16984/saufenbilder.341517

Abstract

In this
study, we determine generating differential invariants for  curves, which is shown to be fonctionally
independent. In addition, using these diffenrial invariants, the equivalence
problem of two families of  curves in  is investigated.

Keywords

affine differential geometry invariant curves

References

  • R.G. Aripov, D. Khadjiev, The Complete system of global differential and integral invariants of a curve in Euclidean geometry, Russian Mathematics, vol. 51, no. 7, pp. 1-14, 2007.
  • W. Blaschke, Affine Differentialgeometrie, Springer, Berlin, 1923.
  • R.B. Gardner, G.R. Wilkens, The fundamental theorems of curves and hypersurfaces in centro-affine geometry, Bull. Belg. Math. Soc., vol. 4, pp. 379-401, 1997.
  • S. Izumiya, T. Sano, Generic afine differential geometry of space curves, Proceedings of the Royal Society of Edinburg, vol. 128, no. A, pp. 301-314, 1998.
  • D. Khadjiev, The Application of Invariant Theory to Differential Geometry of Curves. Fan Publ, Tashkent, 1988.
  • D. Khadjiev, Ö. Pekşen, The Complete system of global differential and integral invariants for equi-affine curves, Differential Geom. Appl., vol. 20, pp. 167-175, 2004.
  • H. Liu, Curves in affine and semi-Euclidean Spaces, Result. Math., vol. 65, pp. 235-249, 2014.
  • Y. Sağıroğlu, Affine Differential Invariants of Curves: The Equivalence of Parametric Curves in Terms of Invariants. LAP LAMBERT Academic Publishing, 2012.
  • Y. Sağıroğlu, The Equivalence problem for parametric curves in one-dimensional affine space, Int. Math. Forum, vol. 6, no. 4, pp. 177-184, 2011.
  • P.A. Schirokow, A.P. Schirokow, Affine Differentialgeometrie, Teubner, Leipzig, 1962.
  • B. Su, Affine Differential Geometry, Science Press, Beijing, 1983.
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Uğur Gözütok

Yasemin Sağıroğlu This is me

Publication Date June 1, 2018
Submission Date October 3, 2017
Acceptance Date May 9, 2018
Published in Issue Year 2018 Volume: 22 Issue: 3

Cite

APA Gözütok, U., & Sağıroğlu, Y. (2018). R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları. Sakarya University Journal of Science, 22(3), 1007-1014. https://doi.org/10.16984/saufenbilder.341517
AMA Gözütok U, Sağıroğlu Y. R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları. SAUJS. June 2018;22(3):1007-1014. doi:10.16984/saufenbilder.341517
Chicago Gözütok, Uğur, and Yasemin Sağıroğlu. “R^2 De Bir N-Li Eğri Ailesinin Afin Diferansiyel İnvaryantları”. Sakarya University Journal of Science 22, no. 3 (June 2018): 1007-14. https://doi.org/10.16984/saufenbilder.341517.
EndNote Gözütok U, Sağıroğlu Y (June 1, 2018) R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları. Sakarya University Journal of Science 22 3 1007–1014.
IEEE U. Gözütok and Y. Sağıroğlu, “R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları”, SAUJS, vol. 22, no. 3, pp. 1007–1014, 2018, doi: 10.16984/saufenbilder.341517.
ISNAD Gözütok, Uğur - Sağıroğlu, Yasemin. “R^2 De Bir N-Li Eğri Ailesinin Afin Diferansiyel İnvaryantları”. Sakarya University Journal of Science 22/3 (June 2018), 1007-1014. https://doi.org/10.16984/saufenbilder.341517.
JAMA Gözütok U, Sağıroğlu Y. R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları. SAUJS. 2018;22:1007–1014.
MLA Gözütok, Uğur and Yasemin Sağıroğlu. “R^2 De Bir N-Li Eğri Ailesinin Afin Diferansiyel İnvaryantları”. Sakarya University Journal of Science, vol. 22, no. 3, 2018, pp. 1007-14, doi:10.16984/saufenbilder.341517.
Vancouver Gözütok U, Sağıroğlu Y. R^2 de Bir n-li Eğri Ailesinin Afin Diferansiyel İnvaryantları. SAUJS. 2018;22(3):1007-14.
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