Timelike Factorable Surfaces in Minkowski Space-Time

Year 2018, Volume: 22 Issue: 6, 1939 - 1946, 01.12.2018

Sezgin Büyükkütük

https://doi.org/10.16984/saufenbilder.451646

Abstract

In this study, we discuss timelike factorable surfaces in
Minkowski 4-space E_1^4. We calculate Gaussian and mean curvatures of these
surfaces and classify timelike flat and minimal factorable surfaces in
Minkowski space-time.

Keywords

factorable surface, timelike surface, Minkowski 4-space

References

• [1] B.Y. Chen and J. Van der Veken, “Marginally trapped surfaces in Lorentzian space forms with positive relative nullity,” Class. Quantum Grav., vol. 24, pp. 551–563, 2007.
• [2] G. Ganchev, “Timelike surfaces with zero mean curvature in Minkowski space,” Israel J. of Math., vol. 196, pp. 413–433, 2013.
• [3] B. Bektaş, U. Dursun, “Timelike rotational surface of elliptic, hyperbolic and parabolic types in Minkowski space with pointwise type Gauss map,” Filomat, vol. 29, no. 3, pp. 381–392, 2015.
• [4] B. Y. Chen, “Geometry of Submanifolds,” Marcel Dekker, NewYork, 1973.
• [5] I. Van de Woestyne, “A new characterization of helicoids,” Geometry and Topology of Submanifolds V., World Sci. Publ. River Edge, NJ, 1993.
• [6] I. Van de Woestyne, “Minimal homothetical hypersurfaces of a semi-Euclidean space,” Results Math, vol. 27, no. 3, pp. 333–342, 1995.
• [7] R. Lopez, M. Moruz, “Translation and homothetical surfaces in Euclidean spaces with constant curvature,” J. Korean Math. Soc., vol. 52, no. 3, pp. 523–535, 2015.
• [8] H. Meng, H. Liu, “Factorable surfaces in Minkowski space,” Bull. Korean Math. Soc., vol. 46, no. 1, pp. 155–169, 2009.
• [9] Y. Yu, H. Liu, “The factorable minimal surfaces ,” Proceedings of The Eleventh International Workshop on Diff. Geom., vol. 11, pp. 33–39, 2007.
• [10] Y. A. Aminov, “Surfaces in with a Gaussian curvature coinciding with a Gaussian torsion up to sign,” Mathematical Notes, vol. 56, pp. 5–6, 1994.
• [11] B. Bulca, K. Arslan, “Surfaces given with the Monge patch in ,” Journal of Mathematical Physics, Analysis, Geometry, vol. 9, no. 4, pp. 435–447, 2013.
• [12] K. Arslan, B. K. Bayram, B. Bulca, G. Öztürk, “Generalized rotational surfaces in ,” Results in Mathematics, vol. 61, no. 3-4, pp. 315-327, 2012.
• [13] K. Arslan, B. K. Bayram, B. Bulca, Y.H. Kim, C. Murathan, G. Öztürk, “Rotational embeddings in with pointwise 1-type Gauss map, ” Turk J. Math., vol. 35, pp. 493-499, 2011.
• [14] K. Arslan, B. Bulca, B. K. Bayram, Y. H. Kim, C. Murathan, G. Öztürk, “Tensor product surfaces with pointwise 1-type Gauss map,” Bull. Korean Math. Soc., vol. 48, no. 3, pp. 601–609, 2011.
• [15] K. Arslan, B. K. Bayram, B. Bulca, Y.H. Kim, C. Murathan, G. Öztürk, “ Vranceanu surface in with pointwise 1-type Gauss map, ” Indian J. Pure Appl. Math., vol. 42, no. 1, pp. 41-51, 2011.
• [16] E. İyigün, K. Arslan, G. Öztürk, “ A characterization of Chen surfaces in ,” Bull. Malays. Math. Soc., vol. 31, no. 2, pp. 209-215, 2008.