TY  - JOUR
T1  - Rotational surfaces with Cheng-Yau operator in Galilean 3-spaces
AU  - Kelleci Akbay, Alev
PY  - 2021
DA  - April
DO  - 10.15672/hujms.612730
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 365
EP  - 376
VL  - 50
IS  - 2
LA  - en
AB  - In this paper, we study three types of rotational surfaces in Galilean 3-spaces. We classify rotational surfaces satisfying $$L_1G=F(G+C)$$for some constant vector $C\in \mathbb{G}^3$ and smooth function $F$, where $L_1$ denotes the Cheng-Yau operator.
KW  - Cheng-Yau operator
KW  - Rotational surfaces
KW  - Galilean spaces
KW  - $L_1$-pointwise 1-type
CR  - [1] L.J. Alias and N. Gurbuz, An extension of Takashi theorem for the linearized operators
of the highest order mean curvatures, Geom. Dedicata 121, 113-127, 2006.
CR  - [2] M.E. Aydin, A.O. Oğrenmis and M. Ergut, Classification of factorable surfaces in the
pseudo-Galilean space, Glas. Mat. Ser. III 50 (2), 441-451, 2015.
CR  - [3] B.Y. Chen, Total mean curvature and submanifolds finite type, World Scientific Publ.,
New Jersey, 1984.
CR  - [4] B.Y. Chen, A report on submanifolds of finite type, Soochow J. Math. 22, 117-337,
1996.
CR  - [5] B.Y. Chen, M. Choi, and Y.H. Kim, Surfaces of revolution with pointwise 1-type
Gauss map, J. Korean Math. Soc. 42, 447-455, 2005.
CR  - [6] B.Y. Chen, J. Morvan and T. Nore, Energy, tension and finite type maps, Kodai
Math. J. 9, 406-418, 1986.
CR  - [7] B.Y. Chen, and P. Piccinni, Submanifolds with finite type Gauss map, Bull. Austral.
Math. Soc. 35 (2), 161-186, 1987.
CR  - [8] S.Y. Cheng and S.T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann.
225, 195-204, 1977.
CR  - [9] M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18, 209-217, 2013.
CR  - [10] M. Dede, C. Ekici and W. Goemans, Surfaces of revolution with vanishing curvature
in Galilean 3-space, J. Math. Physics, Analysis, Geometry 14 (2), 141-152, 2018.
CR  - [11] U. Dursun, Hypersurfaces with pointwise 1-type Gauss map, Taiwanese J. Math. 11
(5), 1407-1416, 2007.
CR  - [12] S.M.B. Kashani, On some $L_1-$finite type (hyper)surfaces in $\mathbb R^{n+1}$, Bull. Korean Math.
Soc. 46 (1), 35-43, 2009.
CR  - [13] U.H. Ki, D.S. Kim, Y. H. Kim and Y.M. Roh, Surfaces of revolution with pointwise
1-type Gauss map in Minkowski 3-space, Taiwan. J. Math. 13 (1), 317-338, 2009.
CR  - [14] D.S. Kim, J.R. Kim and Y. H. Kim, Cheng-Yau operator and Gauss map of surfaces
of revolution, Bull. Malays. Math. Sci. Soc. 39 (4), 1319-1327, 2016.
CR  - [15] Y.H. Kim and N.C. Turgay, Surfaces in $\mathbb{E}^3$ with $L_1-$pointwise 1-type Gauss map,
Bull. Korean Math. Soc. 50 (3), 935-949, 2013.
CR  - [16] Y.H. Kim and N.C. Turgay, On the helicoidal surfaces in $\mathbb{E}^3$ with $L_1-$pointwise 1-type
Gauss map, Bull. Korean Math. Soc. 50, 1345-1356, 2013.
CR  - [17] Y.H. Kim and D.W. Yoon, Ruled surfaces with pointwise 1-type Gauss map, J. Geom.
Phys. 34 (3-4), 191-205, 2000.
CR  - [18] Z.M. Sipus, Ruled Weingarten surfaces in Galilean space, Period. Math. Hungar. 56,
213-225, 2008.
CR  - [19] Z.M. Sipus and B. Divjak, Translation surfaces in the Galilean space, Glas. Mat.
Ser. III 46, No. 66, 455-469, 2011.
CR  - [20] Z.M. Sipus, and B. Divjak, Surfaces of constant curvature in pseudo-Galilean space,
Int. J. Math. Sci. 2012, Art. ID 375264, 28 pp, 2012.
CR  - [21] D. Palman, Drehyzykliden des Galileischen Raumes $G_3$, Math. Pannon. 2 (1), 98-104,
1991.
UR  - https://doi.org/10.15672/hujms.612730
L1  - https://dergipark.org.tr/en/download/article-file/795798
ER  -