Browse > Article
http://dx.doi.org/10.5666/KMJ.2022.62.1.167

Classifications of Tubular Surface with L1-Pointwise 1-Type Gauss Map in Galilean 3-space 𝔾3  

Kisi, Ilim (Department of Mathematics, Kocaeli University)
Ozturk, Gunay (Department of Mathematics, Izmir Democracy University)
Publication Information
Kyungpook Mathematical Journal / v.62, no.1, 2022 , pp. 167-177 More about this Journal
Abstract
In this manuscript, we handle a tubular surface whose Gauss map G satisfies the equality L1G = f(G + C) for the Cheng-Yau operator L1 in Galilean 3-space 𝔾3. We give an example of a tubular surface having L1-harmonic Gauss map. Moreover, we obtain a complete classification of tubular surface having L1-pointwise 1-type Gauss map of the first kind in 𝔾3 and we give some visualizations of this type surface.
Keywords
Cheng-Yau operator; Gauss map; tubular surface; Galilean 3-space;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 I. Kisi and G. Ozturk, A new approach to canal surface with parallel transport frame, Int. J. Geom. Methods Mod. Phys., 14(2)(2017), 1-16.
2 I. Kisi and G. Ozturk, Tubular surface having pointwise 1-type Gauss map in Euclidean 4-space, Int. Electron. J. Geom., 12(2019), 202-209.   DOI
3 I. Kisi, G. Ozturk and K. Arslan, A new type of canal surface in Euclidean 4-space 𝔼4, Sakarya University Journal of Science, 23(2019), 801-809.   DOI
4 G. Ozturk, B. Bulca, B. K. Bayram and K. Arslan, On canal surfaces in 𝔼3, Selcuk J. Appl. Math., 11(2010), 103-108.
5 B. J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space 𝔾3, Glas. Mat. Ser. III, 22(1987), 449-457.
6 O. Roschel, Die Geometrie Des Galileischen Raumes, Forschungszentrum Graz Research Centre, Austria(1986).
7 I. M. Yaglom, A simple non-Euclidean geometry and its physical basis, Springer-Verlag Inc., New York(1979).
8 A. T. Ali, Position vectors of curves in the Galilen Space 𝔾3, Matematicki Vesnik, 64(2012), 200-210.
9 L. J. Alias and N. Gurbuz, An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Dedicata, 121(2006), 113-127.   DOI
10 K. Arslan, B. (Kilic) Bayram, B. Bulca, Y. H. Kim, C. Murathan and G. Ozturk, Vranceanu surface in 𝔼4 with pointwise 1-type Gauss map, Indian J. Pure Appl. Math., 42(2011), 41-51.   DOI
11 B. Bulca, K. Arslan, B. Bayram and G. Ozturk, Canal surfaces in 4-dimensional Euclidean Space, Libertas Mathematica, 32(2012), 1-13.   DOI
12 B. Y. Chen and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc., 35(1987), 161-186.   DOI
13 S. Y. Cheng and S. T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann., 225(1977), 195-204.   DOI
14 S. M. B. Kashani, On some L1-finite type (hyper)surfaces in ℝn+1, Bull. Korean Math. Soc., 46(2009), 35-43.   DOI
15 J. Qian and Y. H. Kim, Classifications of canal surfaces with L1-pointwise 1-type Gauss map, Milan J. Math., 83(1)(2015), 145-155.   DOI
16 K. Arslan and B. (Kilic) Bayram, B. Bulca, Y. H. Kim, C. Murathan and G. Ozturk, Rotational embeddings in 𝔼4 with pointwise 1-type Gauss map, Turk. J. Math., 35(2011), 493-499.   DOI
17 B. Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics, 1. World Scientific Publishing Co., Singapore(1984).
18 M. Dede, Tubular surfaces in Galilean space, Math. Commun., 18(1)(2013), 209-217.
19 Y. H. Kim and N. C. Turgay, Surfaces in 𝔼3 with L1-pointwise 1-type Gauss map, Bull. Korean Math. Soc., 50(3)(2013), 935-949.   DOI
20 Y. H. Kim and N. C. Turgay, On the ruled surfaces with L1-pointwise 1-type Gauss map, Kyungpook Math. J., 57(1)(2017), 133-144.   DOI