Centro-Equiaffine Differential Invariants of Curve Families

Year 2016, Volume: 9 Issue: 1, 23 - 29, 30.04.2016

Yasemin Sağıroğlu

https://doi.org/10.36890/iejg.591882

Cited By: 1

Abstract

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.

Keywords

Differential invariant, parametric curve, equivalence

References

• [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.