Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density

Kazan, Ahmet; Karadag, H. Bayram

doi:10.28924/2291-8639-16-2018-414

Research Article

Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density

Ahmet Kazan¹*
H. Bayram Karadag

Inonu University

* Corresponding author

Abstract

In this paper, we obtain the weighted mean and weighted Gaussian curvatures of surfaces of revolution in Galilean 3-space with density $e^{a_{1}x^{2}+a_{2}y^{2}+a_{3}z^{2}}$, $a_{1},a_{2},a_{3} \in R$ not all zero. Also, we investigate some cases of weighted minimal surfaces of revolution according to $a_{i},$ $i=1,2,3$ and weighted flat surfaces of revolution.

How to Cite

A. Kazan, H. B. Karadag, Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density, Int. J. Anal. Appl. 16 (2018), 414–426. https://doi.org/10.28924/2291-8639-16-2018-414

BibTeX

@article{Kazan2018,
  author  = {Kazan, Ahmet and Karadag, H. Bayram},
  title   = {Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {414--426},
  doi     = {10.28924/2291-8639-16-2018-414}
}

References

[1] M. Bekkar and H. Zoubir, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆xi= λixi, Int. J. Contemp. Math. Sci. 24 (3) (2008), 1173-1185.
[2] I. Corwin, H. Hoffman, S. Hurder, V. Ssum and Y. Xu, Differential geometry of manifolds with density, Rose-Hulman Und. Math. J. 7 (2006), 1-15.
[3] M. Dede, C. Ekici and W. Goemans, Surfaces of Revolution with Vanishing Curvature in Galilean 3-Space, J. Math. Phys. in press.
[4] M. Dede, Tubular Surfaces in Galilean Space, Math. Commun. 18 (2013), 209-217.
[5] F. Dillen, J. Pas and L. Verstraelen, On the Gauss map of surfaces of revolution, Bull. Inst. Math. Acad. Sinica 18 (1990), 239-246.
[6] B. Divjak and Z.M. Sipus, Some Special Surfaces in the Pseudo-Galilean Space, Acta Math. Hungar. 118 (3) (2008), 209-226.
[7] A. Ferrandez and P. Lucas, On Surfaces in the 3-dimensional Lorentz-Minkowski space, Pac. J. Math. 152 (1) (1992), 93-100.
[8] O.J. Garay, On a certain class of finite type surfaces of revolution, Kodai Math. J. 11 (1) (1988), 25-31.
[9] M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Func. Anal. 13 (2003), 178-215.
[10] D.T. Hieu and N.M Hoang, Ruled minimal surfaces in R3with density ez, Pac. J. Math. 243 (2009), 277-285.
[11] G. Kaimakamis and B. Papantoniou, Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆II~r = A~r, J. Geom. 81 (2004), 81-92.
[12] A. Kazan and H.B. Karada˘ g, A Classification of Surfaces of Revolution in Lorentz-Minkowski Space, Int. J. Contemp. Math. Sci. 39 (6) (2011), 1915-1928.
[13] D-S. Kim and D.W. Yoon, Constructions of Helicoidal Surfaces in Euclidean Space with Density, Symmetry 9 (2017), Art. ID 173.
[14] S. Lee and J.H. Varnado, Spacelike constant mean curvature surfaces of revolution in Minkowski 3-space, Differ. Geom. Dyn. Syst. 8 (1) (2006), 144-165.
[15] R. López, Minimal surface in Euclidean Space with a Log-Linear Density, arXiv:1410.2517
[math.DG] (accessed on 20 July 2017).
[16] O. Röschel, Die Geometrie des Galileischen Raumes, Bericht der Mathematisch-Statistischen Sektion in der Forschungsge- sellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, (1984).
[17] Z.M. Sipus, Ruled Weingarten Surfaces in the Galilean Space, Period. Math. Hung. 56 (2) (2008), 213-225.
[18] D.W. Yoon, Weighted Minimal Translation Surfaces in the Galilean Space with Density, Open Math. 15 (2017), 459-466.