Journals / International Electronic Journal of Geometry / 2026 / Volume: 12 Issue: 1

Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity

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2019-03-27
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In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean
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Key Findings & Data:In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean
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Conclusion & Impact:In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Minkowski space · manifold with density · weighted curvature

Abstract

In this paper, we construct a helicoidal surface of type III+ with prescribed weighted mean

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Cite This Article

Yıldız, Ö. G., Akyiğit, M. (2019). Constructions of Type III+ Helicoidal Surfaces in Minkowski Space with Desity. International Electronic Journal of Geometry, Volume: 12 Issue: 1. https://ajindex.com/articles/1411165

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References (22)

  1. Baba-Hamed, C. and Bekkar, M., Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying4II ri = iri. J. Geom. 100 (2011), no. 1-2, 1.
  2. Baikoussis, C. and Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature. J. Geom. 63 (1998), no. 1, 25-29.
  3. Beneki, C.C., Kaimakamis, G. and Papantoniou, B.J., Helicoidal surfaces in three-dimensional Minkowski space. Journal of Mathematical Analysis and Applications, 275 (2002), no. 2, 586-614.
  4. Corro, A. V., Pina, R. and Souza, M., Surfaces of rotation with constant extrinsic curvature in a conformally flat 3-space. Results in Mathematics, 60 (2011), no. 1-4, 225.
  5. Corwin, I., Hoffman, N., Hurder, S., Šešum, V. and Xu, Y., Differential geometry of manifolds with density. Rose-Hulman Undergrad. Math. J., 7(2006), 1-15.
  6. Delaunay, C. H., Sur la surface de révolution dont la courbure moyenne est constante. Journal de mathématiques pures et appliquées (1841), 309-314.
  7. Do Carmo, M.P. and Dajczer, M., Helicoidal surfaces with constant mean curvature. Tohoku Mathematical Journal, Second Series 34 (1982), no. 3, 425-435.
  8. Hıeu, D.T. and Hoang, N.M., Ruled minimal surfaces in R3 with density ez. Pacific Journal of Mathematics, 243 (2009), no. 2, 277-285.
  9. Hou, Z.H. and Ji, F., Helicoidal surfaces with H2 = K in Minkowski 3-space. Journal of mathematical analysis and applications, 325 (2007), no. 1, 101-113.
  10. Ji, F. and Hou, Z.H., A kind of helicoidal surfaces in 3-dimensional Minkowski space. Journal of mathematical analysis and applications, 304 (2005), no.2 632-643.
  11. Ji, F. and Hou, Z.H., Helicoidal surfaces under the cubic screw motion in Minkowski 3-space. Journal of mathematical analysis and applications, 318 (2006), no. 2, 634-647.
  12. Morgan, F., Geometric measure theory: a beginner’s guide. Academic press, 2016.
  13. Morgan, F., Manifolds with density. Notices of the AMS, (2005), 853-858.
  14. Morgan, F., Myers’ theorem with density. Kodai Mathematical Journal, 29 (2006), no. 3, 455-461.
  15. Morgan, F., Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture. American Mathematical Monthly, 116 (2009), no. 2, 134-142.
  16. Rafael, L. and Demir, E., Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature. Open Mathematics, 12 (2014), no: 9, 1349-1361.
  17. Rayón, P. and Gromov, M., Isoperimetry of waists and concentration of maps. Geometric and functional analysis, 13 (2003), no. 1, 178-215.
  18. Rosales, C., Cañete, A., Bayle, V. and Morgan, M., On the isoperimetric problem in Euclidean space with density. Calculus of Variations and Partial Differential Equations, 31 (2008), no. 1, 27-46.
  19. Roussos, I.M., The helicoidal surfaces as Bonnet surfaces. Tohoku Mathematical Journal, Second Series 40 (1988), no. 3, 485-490.
  20. Yıldız, Ö.G., Hızal, S. and Akyi˘ git, M., Type I+ Helicoidal Surfaces with PrescribedWeighted Mean or Gaussian Curvature in Minkowski Space with Density. Analele Universitatii" Ovidius" Constanta-Seria Matematica, 26 (2018), no. 3, 99-108.
  21. Yoon, D.W.,Weighted minimal translation surfaces in Minkowski 3-space with density. International Journal of Geometric Methods in Modern Physics, 14 (2017), no. 12, 1750178.
  22. Yoon, D.W., Kim, D.S., Kim, Y.H. and Lee, J.W., Constructions of Helicoidal Surfaces in Euclidean Space with Density. Symmetry 9 (2017), no. 9, 173.