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Eğri Ailelerinin GL(n,R) deki Denklikleri ve Diferansiyel İnvaryantlar

Year 2018, Volume: 8 Issue: 2, 348 - 357, 31.07.2018
https://doi.org/10.17714/gumusfenbil.398292

Abstract

Bu çalışmada {x_1,x_2,...,x_m} parametrik eğrileriyle oluşturulan R<x_1,x_2,...,x_m>^GL(n,R) kümesinin üreteç kümesi bulunmuştur. Herhangi
iki eğri ailesinin GL(n,R)
-denklik koşulları, bu üreteç diferansiyel
invaryantlar kullanılarak elde edilmiştir. Ayrıca üreteç sisteminin minimal
olduğu gösterilmiştir. 

References

  • Gardner, R.B., ve Wilkens, G.R., 1997. The fundamental theorems of curves and hypersurfaces in centro-affine geometry. Bull. Belg. Math. Soc., 4, 379-401.
  • Giblin, P.J., ve Sano, T., 2012. Generic equi-centro-affine differential geometry of plane curves. Topology Appl., 159, 476-483.
  • Izumiya, S., ve Sano, T., 2000. Generic affine differential geometry of space curves. Proceedings of the Royal Soc. of Edinburgh, 128A, 301-314.
  • İncesu, M., ve Gürsoy, O., 2017. LS(2)-Equivalence conditions of control points and application to planar Bezier curves. NTMSCI, 5(3), 70-84.
  • Khadjiev, Dj., ve Pekşen, Ö., 2004. The complete system of global differential and integral invariants for equi-affine curves. Diff. Geom. Appl., 20, 167-175.
  • Nadjafikhah, M., 2002. Affine differential invariants for planar curves. Balk. J. Geom. Appl., 7, 69-78.
  • Olver, P.J., 2010. Moving frames and differential invariants in centro-affine geometry. Lobachevskii J. Math., 31, 77-89.
  • Pekşen, Ö., ve Khadjiev, D., 2004. On invariants of curves in centro-affine geometry. J. Math. Kyoto Univ., 44(3), 603-613.
  • Sağıroğlu, Y., 2012. Affine Differential Invariants of Curves. LAP, Saarbrücken, 128p.
  • Sağıroğlu, Y., 2016. Centro-equiaffine differential invariants of curve families. IEJG, 9, 23-29.
  • Sağıroğlu, Y., 2015. Equi-affine differential invariants of a pair of curves. TWMS J. Pure. Appl. Math., 6, 238-245.
  • Sağıroğlu, Y., ve Pekşen, Ö., 2010. The equivalence of equi-affine curves. Turk. J. Math., 34, 95-104.
  • Sağıroğlu, Y., ve Yapar, Z. 2016. GL(n,R)-Equivalence of a pair of curves in terms of invariants. Journal of Mathematics and System Science, 6, 16-22.
  • Sibirskii, K.S., 1976. Algebraic invariants of differential equations and matrices, Kishinev, Stiintsa, 268p.

Equivalence of Curve Families in GL(n,R) and Differential Invariants

Year 2018, Volume: 8 Issue: 2, 348 - 357, 31.07.2018
https://doi.org/10.17714/gumusfenbil.398292

Abstract

In this study, the generating system of the set  R<x_1,x_2,...,x_m>^GL(n,R) formed by the parametric curves {x_1,x_2,...,x_m} is obtained. The conditions of  GL(n,R)-equivalence of two curve families are given by means of the differential
invariants. It is also shown that the generating system is minimal.

References

  • Gardner, R.B., ve Wilkens, G.R., 1997. The fundamental theorems of curves and hypersurfaces in centro-affine geometry. Bull. Belg. Math. Soc., 4, 379-401.
  • Giblin, P.J., ve Sano, T., 2012. Generic equi-centro-affine differential geometry of plane curves. Topology Appl., 159, 476-483.
  • Izumiya, S., ve Sano, T., 2000. Generic affine differential geometry of space curves. Proceedings of the Royal Soc. of Edinburgh, 128A, 301-314.
  • İncesu, M., ve Gürsoy, O., 2017. LS(2)-Equivalence conditions of control points and application to planar Bezier curves. NTMSCI, 5(3), 70-84.
  • Khadjiev, Dj., ve Pekşen, Ö., 2004. The complete system of global differential and integral invariants for equi-affine curves. Diff. Geom. Appl., 20, 167-175.
  • Nadjafikhah, M., 2002. Affine differential invariants for planar curves. Balk. J. Geom. Appl., 7, 69-78.
  • Olver, P.J., 2010. Moving frames and differential invariants in centro-affine geometry. Lobachevskii J. Math., 31, 77-89.
  • Pekşen, Ö., ve Khadjiev, D., 2004. On invariants of curves in centro-affine geometry. J. Math. Kyoto Univ., 44(3), 603-613.
  • Sağıroğlu, Y., 2012. Affine Differential Invariants of Curves. LAP, Saarbrücken, 128p.
  • Sağıroğlu, Y., 2016. Centro-equiaffine differential invariants of curve families. IEJG, 9, 23-29.
  • Sağıroğlu, Y., 2015. Equi-affine differential invariants of a pair of curves. TWMS J. Pure. Appl. Math., 6, 238-245.
  • Sağıroğlu, Y., ve Pekşen, Ö., 2010. The equivalence of equi-affine curves. Turk. J. Math., 34, 95-104.
  • Sağıroğlu, Y., ve Yapar, Z. 2016. GL(n,R)-Equivalence of a pair of curves in terms of invariants. Journal of Mathematics and System Science, 6, 16-22.
  • Sibirskii, K.S., 1976. Algebraic invariants of differential equations and matrices, Kishinev, Stiintsa, 268p.
There are 14 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Yasemin Sağıroğlu This is me 0000-0003-0660-211X

Uğur Gözütok 0000-0002-6072-3134

Publication Date July 31, 2018
Submission Date February 24, 2018
Acceptance Date April 17, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

Cite

APA Sağıroğlu, Y., & Gözütok, U. (2018). Eğri Ailelerinin GL(n,R) deki Denklikleri ve Diferansiyel İnvaryantlar. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 8(2), 348-357. https://doi.org/10.17714/gumusfenbil.398292