KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2016 / Cilt: 9 - Sayı: 2

Differential Geometry of Rectifying Submanifolds Bang-Yen Chen (Communicated by Kazım ?Ilarslan)

Bang-Yen CHEN
Sayfa
1–8
Yayın Tarihi
2022-10-18
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)

Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:A space curve in a Euclidean 3-space E3is called a rectifying curve if its position vector fieldalways lies in its rectifying plane.
📊
Temel Bulgular & Veri:Monthly 110 (2003), no. 2, 147-152].
💡
Sonuç & Katkı:Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.
🔬Tür:Araştırma Makalesi
📍Kapsam:2003 Verileri
⚙️Değişkenler:Alan Parametreleri

Abstract

A space curve in a Euclidean 3-space E3is called a rectifying curve if its position vector fieldalways lies in its rectifying plane. This notion of rectifying curves was introduced by the authorin [Amer. Math. Monthly 110 (2003), no. 2, 147-152]. In this present article, we introduce andstudy the notion of rectifying submanifolds in Euclidean spaces. In particular, we prove that aEuclidean submanifold is rectifying if and only if the tangential component of its position vectorfield is a concurrent vector field. Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.

🔖

Bu Makaleye Atıf Yap

CHEN, B. (2022). Differential Geometry of Rectifying Submanifolds Bang-Yen Chen (Communicated by Kazım ?Ilarslan). International Electronic Journal of Geometry, Cilt: 9 - Sayı: 2, 1–8. https://ajindex.com/articles/539711

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. Cambie, S., Goemans, W. and Van den Bussche, I., Rectifying curves in the n-dimensional Euclidean space. Turkish J. Math. 40 (2016), no., 210-223.
  2. Chen, B.-Y., Geometry of Submanifolds. Marcel Dekker, New York, 1973.
  3. Chen, B.-Y., Constant-ratio hypersurfaces. Soochow J. Math. 21 (2001), 353-361.
  4. Chen, B.-Y., Geometry of position functions of Riemannian submanifolds in pseudo-Euclidean space. J. Geom. 74 (2002), 61-77.
  5. Chen, B.-Y., Convolution of Riemannian manifolds and its applications. Bull. Austral. Math. Soc. 66 (2002), no. 2, 177-191.
  6. Chen, B.-Y., When does the position vector of a space curve always lie in its rectifying plane?. Amer. Math. Monthly 110 (2003), no. 2, -152. Chen, B.-Y., More on convolution of Riemannian manifolds. Beiträge Algebra Geom. 44 (2003), 9-24.
  7. Chen, B.-Y., Constant-ratio space-like submanifolds in pseudo-Euclidean space. Houston J. Math. 29 (2003), no. 2, 281-294
  8. Chen, B.-Y., Pseudo-Riemannian geometry, ?-invariants and applications. World Scientific, 2011.
  9. Chen, B.-Y., Topics in differential geometry associated with position vector fields on Euclidean submanifolds. Arab J. Math. Sci. 23 (2017), no. 1 (Special Issue on Geometry and Global Analysis), doi:10.1016/j.ajmsc.2016.08.001. Chen, B.-Y. and Dillen, F., Rectifying curves as centrodes and extremal curves. Bull. Inst. Math. Acad. Sinica 33 (2005), no. 2, 77-90.
  10. Gungor, M. A. and Tosun, M., Some characterizations of quaternionic rectifying curves. Differ. Geom. Dyn. Syst. 13 (2011), 89-100.
  11. S. Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), no. 3, 209-215.
  12. Ilarslan, K., Nesovic, E. and Petrovic-Torgasev, M., Some characterizations of rectifying curves in the Minkowski 3-space. Novi Sad J. Math. (2003), no. 2, 23-32.
  13. Ilarslan, K. and Nesovic, E., On rectifying curves as centrodes and extremal curves in the Minkowski 3-space. Novi Sad J. Math. 37 (2007), no. 1, 53-64.
  14. Ilarslan, K. and Nesovic, E., Some characterizations of rectifying curves in the Euclidean space E4. Turkish J. Math. 32 (2008), no. 1, 21-30.
  15. Ilarslan, K. and Nesovic, E., Some relations between normal and rectifying curves in Minkowski space-time. Int. Electron. J. Geom. 7 (2014), no. 1, 26-35.
  16. Lucas, P. and Ortega-Yagues, J. A., Rectifying curves in the three-dimensional sphere. J. Math. Anal. Appl. 421 (2015), no. 2, 1855-1868. Ozbey, and Oral, M., A study on rectifying curves in the dual Lorentzian space. Bull. Korean Math. Soc. 46 (2009), no. 5, 967-978.
  17. Yilmaz, B., Gok