Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 9 Sayı: 1, 23 - 29, 30.04.2016
https://doi.org/10.36890/iejg.591882

Öz

Kaynakça

  • [1] Aripov, R.G., Khadziev, D., The Complete System of Global Differential and Integral Invariants of a Curve in Euclidean Geometry, 51 (2007),no.7, 1-14.
  • [2] Gardner, R.B., Wilkens, G.R., The Fundamental Theorems of Curves and Hypersurfaces in Centro-affine Geometry, Bull.Belg.Math.Soc., 4 (1997), 379-401.
  • [3] Giblin, J.P., Sapiro, G., Affine-invariant distances, envelopes and symmetry sets, Geometriae Dedicata, 71 (1998), 237-261.
  • [4] Guggenheimer, H.W., Differential Geometry, McGraw-Hill, New York, 1963.
  • [5] Hann C.E., Hickman, M.S., Projective Curvature and Integral Invariants, Acta Applicandae Mathematicae, 74 (2002), 177-193.
  • [6] Izumiyma, S., Sano, T., Generic affine differential geometry of space curves, Proceedings of the Royal Society of Edinburgh, 128A (1998), 301-314.
  • [7] Khadjiev, D., The Application of Invariant Theory to Differential Geometry of Curves, Fan Publ., Tashkent, 1988.
  • [8] Khadjiev, D., Peks¸en, Ö., The complete system of global differential and integral invariants for equi-affine curves, Differential Geometry and It’s Applications, 20 (2004), 167-175.
  • [9] Klingenberg W., A Course in Differential Geometry, Springer-Verlag, New York, 1978.
  • [10] Looijenga, E.J.N., Invariants of quartic plane curves as automorphic forms, Contemporary Mathematics, 422 (2007), 107-120.
  • [11] Mokhtarian, F., Abbasi, S., Affine Curvature Space Scale with Affine Length Parametrization, Pattern Analysis & Applications, 4 (2001), 1-8.
  • [12] Nomizu, K., Sasaki, T., Affine Differential Geometry, Cambridge Univ. Pres., 1994.
  • [13] Paukowitsch, H.P., Begleitfiguren und Invariantensystem Minimaler Differentiationsordnung von Kurven im Reellen n-dimensionalen Affinen Raum, Mh. Math., 85 (1978), no.2, 137-148.
  • [14] Pekşen, Ö., Khadjiev, D., On invariants of curves in centro-affine geometry, J. Math. Kyoto Univ., 44 (2004), no.3, 603-613.
  • [15] Sağıroğlu, Y., Global differential invariants of affine curves in R2, Far East Journal of Mathematical Sciences, 96 (2015), no.4, 497-515.
  • [16] Sağıroğlu, Y., The equivalence of curves in SL(n, R) and its application to ruled surfaces, Appl. Math. Comput., 218 (2011), 1019-1024.
  • [17] Schirokow, P.A., Schirokow, A.P., Affine Differential Geometrie, Teubner, Leipzig, 1962.
  • [18] Su, B., Affine Differential Geometry, Science Press, Beijing, Gordon and Breach, New York, 1983.
  • [19] Ünel, M., Wolovich, W.A., On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves, Advances in Applied Mathematics, 24 (2000), 65-87.
  • [20] Weyl, H., The Classical Groups, Princeton Univ. Press, Princeton, NJ, 1946.

Centro-Equiaffine Differential Invariants of Curve Families

Yıl 2016, Cilt: 9 Sayı: 1, 23 - 29, 30.04.2016
https://doi.org/10.36890/iejg.591882

Öz

The generator set of all centro-equiaffine differential invariant rational functions field for arbitrary
curves is obtained. By using these generators, the conditions of equivalence for two curve families
are found. Then the relations between elements of generator set are investigated.

Kaynakça

  • [1] Aripov, R.G., Khadziev, D., The Complete System of Global Differential and Integral Invariants of a Curve in Euclidean Geometry, 51 (2007),no.7, 1-14.
  • [2] Gardner, R.B., Wilkens, G.R., The Fundamental Theorems of Curves and Hypersurfaces in Centro-affine Geometry, Bull.Belg.Math.Soc., 4 (1997), 379-401.
  • [3] Giblin, J.P., Sapiro, G., Affine-invariant distances, envelopes and symmetry sets, Geometriae Dedicata, 71 (1998), 237-261.
  • [4] Guggenheimer, H.W., Differential Geometry, McGraw-Hill, New York, 1963.
  • [5] Hann C.E., Hickman, M.S., Projective Curvature and Integral Invariants, Acta Applicandae Mathematicae, 74 (2002), 177-193.
  • [6] Izumiyma, S., Sano, T., Generic affine differential geometry of space curves, Proceedings of the Royal Society of Edinburgh, 128A (1998), 301-314.
  • [7] Khadjiev, D., The Application of Invariant Theory to Differential Geometry of Curves, Fan Publ., Tashkent, 1988.
  • [8] Khadjiev, D., Peks¸en, Ö., The complete system of global differential and integral invariants for equi-affine curves, Differential Geometry and It’s Applications, 20 (2004), 167-175.
  • [9] Klingenberg W., A Course in Differential Geometry, Springer-Verlag, New York, 1978.
  • [10] Looijenga, E.J.N., Invariants of quartic plane curves as automorphic forms, Contemporary Mathematics, 422 (2007), 107-120.
  • [11] Mokhtarian, F., Abbasi, S., Affine Curvature Space Scale with Affine Length Parametrization, Pattern Analysis & Applications, 4 (2001), 1-8.
  • [12] Nomizu, K., Sasaki, T., Affine Differential Geometry, Cambridge Univ. Pres., 1994.
  • [13] Paukowitsch, H.P., Begleitfiguren und Invariantensystem Minimaler Differentiationsordnung von Kurven im Reellen n-dimensionalen Affinen Raum, Mh. Math., 85 (1978), no.2, 137-148.
  • [14] Pekşen, Ö., Khadjiev, D., On invariants of curves in centro-affine geometry, J. Math. Kyoto Univ., 44 (2004), no.3, 603-613.
  • [15] Sağıroğlu, Y., Global differential invariants of affine curves in R2, Far East Journal of Mathematical Sciences, 96 (2015), no.4, 497-515.
  • [16] Sağıroğlu, Y., The equivalence of curves in SL(n, R) and its application to ruled surfaces, Appl. Math. Comput., 218 (2011), 1019-1024.
  • [17] Schirokow, P.A., Schirokow, A.P., Affine Differential Geometrie, Teubner, Leipzig, 1962.
  • [18] Su, B., Affine Differential Geometry, Science Press, Beijing, Gordon and Breach, New York, 1983.
  • [19] Ünel, M., Wolovich, W.A., On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves, Advances in Applied Mathematics, 24 (2000), 65-87.
  • [20] Weyl, H., The Classical Groups, Princeton Univ. Press, Princeton, NJ, 1946.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Yasemin Sağıroğlu Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 9 Sayı: 1

Kaynak Göster

APA Sağıroğlu, Y. (2016). Centro-Equiaffine Differential Invariants of Curve Families. International Electronic Journal of Geometry, 9(1), 23-29. https://doi.org/10.36890/iejg.591882
AMA Sağıroğlu Y. Centro-Equiaffine Differential Invariants of Curve Families. Int. Electron. J. Geom. Nisan 2016;9(1):23-29. doi:10.36890/iejg.591882
Chicago Sağıroğlu, Yasemin. “Centro-Equiaffine Differential Invariants of Curve Families”. International Electronic Journal of Geometry 9, sy. 1 (Nisan 2016): 23-29. https://doi.org/10.36890/iejg.591882.
EndNote Sağıroğlu Y (01 Nisan 2016) Centro-Equiaffine Differential Invariants of Curve Families. International Electronic Journal of Geometry 9 1 23–29.
IEEE Y. Sağıroğlu, “Centro-Equiaffine Differential Invariants of Curve Families”, Int. Electron. J. Geom., c. 9, sy. 1, ss. 23–29, 2016, doi: 10.36890/iejg.591882.
ISNAD Sağıroğlu, Yasemin. “Centro-Equiaffine Differential Invariants of Curve Families”. International Electronic Journal of Geometry 9/1 (Nisan 2016), 23-29. https://doi.org/10.36890/iejg.591882.
JAMA Sağıroğlu Y. Centro-Equiaffine Differential Invariants of Curve Families. Int. Electron. J. Geom. 2016;9:23–29.
MLA Sağıroğlu, Yasemin. “Centro-Equiaffine Differential Invariants of Curve Families”. International Electronic Journal of Geometry, c. 9, sy. 1, 2016, ss. 23-29, doi:10.36890/iejg.591882.
Vancouver Sağıroğlu Y. Centro-Equiaffine Differential Invariants of Curve Families. Int. Electron. J. Geom. 2016;9(1):23-9.