Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GEOMETRIC CHARACTERIZATIONS OF CANAL SURFACES IN MINKOWSKI 3-SPACE I

  • Fu, Xueshan (Department of Mathematics Northeastern University) ;
  • Jung, Seoung Dal (Department of Mathematics Jeju National University) ;
  • Qian, Jinhua (Department of Mathematics Northeastern University) ;
  • Su, Mengfei (Department of Mathematics Northeastern University)
  • Received : 2018.07.05
  • Accepted : 2018.10.29
  • Published : 2019.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

Keywords

E1BMAX_2019_v56n4_867_f0001.png 이미지

FIGURE 1. Canal sur-face $\mathbb{M}^2_+$ with r(s) = s.

E1BMAX_2019_v56n4_867_f0002.png 이미지

FIGURE 2. Tube $\mathbb{M}^2_+$ with r(s) = 1.

E1BMAX_2019_v56n4_867_f0003.png 이미지

FIGURE 4. Tube $\mathbb{M}^3_+$ with r(s) = 1.

E1BMAX_2019_v56n4_867_f0004.png 이미지

FIGURE 3. Canal sur-face $\mathbb{M}^3_+$ with r(s) = s.

References

  1. M. K. Karacan, D. W. Yoon, and Y. Tuncer, Tubular surface of Weingarten types in Minkowski 3-space, Gen. Math. Notes. 22 (2014), 44-56.
  2. Y. H. Kim, H. Liu, and J. Qian, Some characterizations of canal surfaces, Bull. Korean Math. Soc. 53 (2016), no. 2, 461-477. https://doi.org/10.4134/BKMS.2016.53.2.461
  3. Y. H. Kim and D. W. Yoon, On non-developable ruled surfaces in Lorentz-Minkowski 3-spaces, Taiwanese J. Math. 11 (2007), no. 1, 197-214. https://doi.org/10.11650/twjm/1500404646
  4. R. Lopez, Linear Weingarten surfaces in Euclidean and hyperbolic space, Mat. Contemp. 35 (2008), 95-113.
  5. R. Lopez, Rotational linear Weingarten surfaces of hyperbolic type, Israel J. Math. 167 (2008), 283-301. https://doi.org/10.1007/s11856-008-1049-3
  6. J. Qian and Y. H. Kim, Classifications of canal surfaces with $L_1$-pointwise 1-type Gauss map, Milan J. Math. 83 (2015), no. 1, 145-155. https://doi.org/10.1007/s00032-015-0233-2
  7. J. Qian, M. Su, X. Fu, and S. D. Jung, Geometric characterizations of canal surfaces in Minkowski 3-space II, submitted.
  8. A. Ucum and K. Ilarslan, New types of canal surfaces in Minkowski 3-space, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 449-468. https://doi.org/10.1007/s00006-015-0556-7
  9. Z. Xu, R. Feng, and J. Sun, Analytic and algebraic properties of canal surfaces, J. Comput. Appl. Math. 195 (2006), no. 1-2, 220-228. https://doi.org/10.1016/j.cam.2005.08.002