KaydedilenlerDerginizi ekleyin

Dergiler / Conference Proceedings of Science and Technology / 2018 / Cilt: 1 Sayı: 1

Helicoidal Surfaces Which Have the Timelike Axis in Minkowski Space with Density

Önder Gökmen Yıldız0000-0002-2760-1223
Mahmut Ergüt0000-0002-9098-8280
Mahmut Akyiğit0000-0002-8398-365X
Sayfa
16–19
Yayın Tarihi
2018-12-14
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)

Also we give examples of helicoidal surface with weighted Gaussian curvature.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study the prescribed curvature problem in manifold with density.
📊
Temel Bulgular & Veri:We consider the Minkowski 3-space with a positive density function.
💡
Sonuç & Katkı:Also we give examples of helicoidal surface with weighted Gaussian curvature.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Minkowski space · Helicoidal · Manifold with density

Abstract

In this paper, we study the prescribed curvature problem in manifold with density. We consider the Minkowski 3-space with a positive density function. For a given plane curve and an axis in the plane in Minkowski 3-space, a helicoidal surface can be constructed by the plane curve under helicoidal motions around the axis. Also we give examples of helicoidal surface with weighted Gaussian curvature.

🔖

Bu Makaleye Atıf Yap

Yıldız, Ö. G., Ergüt, M., Akyiğit, M. (2018). Helicoidal Surfaces Which Have the Timelike Axis in Minkowski Space with Density. Conference Proceedings of Science and Technology, Cilt: 1 Sayı: 1, 16–19. https://ajindex.com/articles/984410

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. C. Baba-Hamed, M. Bekkar, Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying $\triangle^{II}r_{i}=\lambda_{i}r_{i}$}, J. Geom., 100(1-2) (2011), 1.
  2. M. P. Do Carmo, M. Dajczer, Helicoidal surfaces with constant mean curvature, Tohoku Math. J., Second Series, 34(3) (1982), 425-435.
  3. L. Rafael, E. Demir, Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature, Open Math., 12(9) (2014), 1349-1361.
  4. I. M. Roussos, The helicoidal surfaces as Bonnet surfaces. Tohoku Math. J., Second Series, 40(3)(1988), 485-490.
  5. C. Baikoussis, T. Koufogiorgos, Helicoidal surfaces with prescribed mean or Gaussian curvature, J. Geom., 63(1) (1998), 25-29.
  6. C. C. Beneki, G. Kaimakamis, B.J. Papantoniou, Helicoidal surfaces in three-dimensional Minkowski space, J. Math. Anal. Appl., 275(2) (2002), 586-614.
  7. F. Ji, Z. H. Hou, A kind of helicoidal surfaces in 3-dimensional Minkowski space, J. Math. Anal. Appl., 304(2) (2005), 632-643.
  8. D. W. Yoon, D. S. Kim, Y.H. Kim, J.W. Lee, Constructions of helicoidal surfaces in Euclidean space with Density, Symmetry, 9(9) (2017), 173.
  9. Ö. G. Yıldız, S. Hızal, M. Akyiğit, Type $I^{+}$ Helicoidal surfaces with prescribed weighted mean or Gaussian curvature in Minkowski space with density, An. Stiint. Univ. Ovidius Constant a, Seria Mat., 26(3) (2018), 99-108.
  10. F. Morgan, Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture, Amer. Math. Monthly, 116(2) (2009), 134-142.
  11. D. T. Hıeu, N.M. Hoang, Ruled minimal surfaces in $\mathbb{R}^{3}$ with density $e^{z}$, Pacific J. Math., 243(2) (2009), 277-285.
  12. F. Morgan, Geometric measure theory: a beginner’s guide, Academic press, 2016.
  13. F. Morgan, Manifolds with density, Notices of the AMS, (2005), 853-858.
  14. F. Morgan, Myers’ theorem with density, Kodai Math. J., 29(3) (2006), 455-461.
  15. P. Rayon, M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Funct. Anal., 13(1) (2003), 178-215.
  16. C. Rosales, A. Cañete, V. Bayle, M. Morgan, On the isoperimetric problem in Euclidean space with density, Calc. Var. Partial Differ. Equ., 31(1) (2008), 27-46.
  17. I. Corwin, N. Hoffman, S. Hurder, V. Šešum, Y. Xu, Differential geometry of manifolds with density, Rose-Hulman Undergrad. Math. J., 7(2006), 1-15.