Abstract
In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space \(\mathbb{E}_2^4\) and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in \(\mathbb{E}_2^4\) and give an example of such surfaces.
Similar content being viewed by others
References
F. Aksoyak and Y. Yayli, Flat Rotational Surfaces with Pointwise 1-Type Gauss Map in E 4, arXiv. 1302.2804, 2013.
K. Arslan, B. K. Bayram, B. Bulca, Y. H. Kim, C. Murathan and G. Öztürk, Rotational Embeddings in E 4 with Pointwise 1-Type Gauss Map, Turk. J. Math., 35 (2011), 493–499.
K. Arslan, B. K. Bayram, Y. H. Kim, C. Murathan and G. Öztürk, Vranceanu Surface in E 4 with Pointwise 1-Type Gauss Map, Indian J. Pure. Appl. Math., 42 (2011), 41–51.
K. Arslan, B. Bulca, B. Kılıç, Y. H. Kim, C. Murathan and G. Öztürk, Tensor Product Surfaces with Pointwise 1-Type Gauss Map, Bull. Korean Math. Soc., 48 (2011), 601–609.
B. Y. Chen, M. Choi and Y. H. Kim, Surfaces of Revolution with Pointwise l-Type Gauss Map, J. Korean Math., 42 (2005), 447–455.
B. Y. Chen and P. Piccinni, Submanifolds with Finite Type-Gauss map, Bull. Austral. Math. Soc., 35 (1987), 161–186.
M. Choi and Y. H. Kim, Characterization of the Helicoid as Ruled Surfaces with Pointwise 1-Type Gauss Map, Bull. Korean Math. Soc., 38 (2001), 753–761.
M. Choi, D. S. Kim and Y. H. Kim, Helicoidal Surfaces with Pointwise 1-Type Gauss Map, J. Korean Math. Soc., 46 (2009), 215–223.
M. Choi and Kim, Y. H. and D. W. Yoon, Classification of Ruled Surfaces with Pointwise 1-Type Gauss Map in Minkowski 3-Space, Taiwanese J. Math., 15 (2011), 1141–1161.
U. Dursun and N. C. Turgay, General Rotational Surfaces in Euclidean Space E 4 with Pointwise 1-Type Gauss Map, Math. Commun., 17 (2012), 71–81.
U. Dursun, Hypersurfaces with Pointwise 1-Type Gauss Map in Lorentz-Minkowski Space, Proc. Est. Acad. Sei., 58 (2009), 146–161.
U. Dursun and E. Coşkun, Flat Surfaces in the Minkowski Space E 31 with Pointwise 1-Type Gauss Map, Turk. J. Math., 36 (2012), 613–629.
U. Dursun and G. G. Arsan, Surfaces in the Euclidean Space E 4 with Pointwise 1-Type Gauss Map, Hacet. J. Math. Stat., 40 (2011), 617–625.
U. Dursun and N. C. Turgay, On Spacelike Surfaces in Minkowski 4-Space with Pointwise 1-Type Gauss Map of Second Type, Balkan J. Geom. App., 17 (2012), 34–45.
Y. H. Kim and D. W. Yoon, Ruled Surfaces with Pointwise 1-iype Gauss Map, J. Geom. Phys., 34 (2000), 191–205.
Y. H. Kim and D. W. Yoon, Classification of Rotation Surfaces in Pseudo Euclidean Space, J. Korean Math., 41 (2004), 379–396.
A. Niang, Rotation Surfaces with 1-Type Gauss Map, Bull. Korean Math. Soc., 42 (2005), 23–27.
A. Niang, On Rotation Surfaces in the Minkowski 3- Dimensional Space with Pointwise 1-Type Gauss Map, J. Korean Math. Soc., 41 (2004), 1007–1021.
D. W. Yoon, Rotation Surfaces with Finite Type Gauss Map in E 4, Indian J. Pure. Appl. Math., 32 (2001), 1803–1808.
D. W. Yoon, Some Properties of The Clifford Torus as Rotation Surface, Indian J. Pure. Appl. Math., 34 (2003), 907–915.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aksoyak, F.K., Yayli, Y. General rotational surfaces with pointwise 1-type Gauss map in pseudo-Euclidean space E 42 . Indian J Pure Appl Math 46, 107–118 (2015). https://doi.org/10.1007/s13226-015-0112-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-015-0112-0