KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1

Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry}

Djavvat KHADJIEV
İdris ÖREN
Ömer PEKŞEN
Sayfa
80–94
Yayın Tarihi
2013-01-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p.
📊
Temel Bulgular & Veri:It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively.
💡
Sonuç & Katkı:A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Key words: Curve · differential invariant · pseudo-Euclidean geometry

Özet

Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively. A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.

Abstract

Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n,p)-invariant differential rational functions of a path (curve), respectively. A fundamental system of relations between elements of the complete system of M(n,p)-invariant differential rational functions of a path (curve) is described.

🔖

Bu Makaleye Atıf Yap

KHADJIEV, D., ÖREN, İ., PEKŞEN, Ö. (2013). Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry}. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 1, 80–94. https://ajindex.com/articles/185701

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (10)

  1. Aslaner, R. and Boran, A. I.: On the geometry of null curves in the Minkowski 4-space. Turkish J. of Math. 32, 1–8 (2008).
  2. Bejancu, A.: Lightlike curves in Lorentz manifolds. Publ. Math. Debrecen. 44, 145–155 (1994). B´ erard B. L. and Charuel X.: A generalization of Frenet’s frame for nondegenerate quadratic forms with any index. In: S´ eminaire de th´ eorie spectrale et g´ eom´ etrie. Ann´ ee 2001–2002, St. Martin d’H´ eres: Universit´ e de Grenoble I, Institut Fourier, S´ emin. Th´ eor. Spectr. G´ eom. 20, 101–130 (2002).
  3. Bini, D., Geralico, A. and Jantzen, R. T.: Frenet-Serret formalism for null world lines. Class. Quantum Grav. 23, 3963–3981 (2006).
  4. Bonnor, W.: Null curves in a Minkowski spacetime. Tensor, N. S. 20, 229–242 (1969). Borisov Yu. F.: Relaxing the a priori constraints of the fundamental theorem of space curves in E n l. Siberian Math J. 38, No. 3, 411–427 (1997). Borisov Yu. F.: On the theorem of natural equations of a curve. Siberian Math. J. 40, No. 4, 617–621 (1999). C ¸ ¨ oken, C. and C ¸ ift¸ci, ¨ U.: On the Cartan curvatures of a null curve in Minkowski spacetime. Geometriae Dedicata. 114, 71–78 (2005).
  5. Duggal, K. L. and Becancu A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Dordrecht, Boston, London. Kluwer Acad. Publ. 1996. Ferr´ andez, A., Gim´ enez, A. and Lucas, P.: Degenerate curves in pseudo-Euclidean spaces of index two. In: Mladenov, Ivailo M. (ed.) et al., Proceedings of the 3rd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 14–23, 2001. Sofia: Coral Press Scientific Publishing. 209–223 (2002). Ferr´ andez, A., Gim´ enez, A. and Lucas, P.: s -degenerate curves in Lorentzian space forms. J. Geom. Phys. 45, No. 1–2, 116–129 (2003).
  6. Formiga, L. B. and Romero, C.: On the differential geometry of time-like curves in Minkowski spacetime. Am. J. Phys. 74(10), 1012–1016 (2006).
  7. Ichimura, H.: Time-like and space-like curves in Frenet-Serret formalisms. Thesis. Hadronic J. Suppl. 3, No. 1, 1–94 (1987).
  8. Inoguchi, J. and Lee, S.: Null curves in Minkowski 3-space, International Electronic Journal of Geometry 1 No. 2, 40–83 (2008).
  9. Kaplansky, I.: An Introduction to Differential Algebra. Paris. Hermann 1957.
  10. Khadjiev, D.: An Application of Invariant Theory to Differential Geometry of Curves, Fan Publ., Tashkent, 1988. [Russian] Khadjiev, D. and Pek¸sen ¨ O.: The complete system of global integral and differential invariants for equi-affine curves. Differential Geometry and i