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Timelike Factorable Surfaces in Minkowski Space-Time

Year 2018, , 1939 - 1946, 01.12.2018
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.

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.
Year 2018, , 1939 - 1946, 01.12.2018
https://doi.org/10.16984/saufenbilder.451646

Abstract

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.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sezgin Büyükkütük 0000-0002-1845-0822

Publication Date December 1, 2018
Submission Date August 7, 2018
Acceptance Date October 30, 2018
Published in Issue Year 2018

Cite

APA Büyükkütük, S. (2018). Timelike Factorable Surfaces in Minkowski Space-Time. Sakarya University Journal of Science, 22(6), 1939-1946. https://doi.org/10.16984/saufenbilder.451646
AMA Büyükkütük S. Timelike Factorable Surfaces in Minkowski Space-Time. SAUJS. December 2018;22(6):1939-1946. doi:10.16984/saufenbilder.451646
Chicago Büyükkütük, Sezgin. “Timelike Factorable Surfaces in Minkowski Space-Time”. Sakarya University Journal of Science 22, no. 6 (December 2018): 1939-46. https://doi.org/10.16984/saufenbilder.451646.
EndNote Büyükkütük S (December 1, 2018) Timelike Factorable Surfaces in Minkowski Space-Time. Sakarya University Journal of Science 22 6 1939–1946.
IEEE S. Büyükkütük, “Timelike Factorable Surfaces in Minkowski Space-Time”, SAUJS, vol. 22, no. 6, pp. 1939–1946, 2018, doi: 10.16984/saufenbilder.451646.
ISNAD Büyükkütük, Sezgin. “Timelike Factorable Surfaces in Minkowski Space-Time”. Sakarya University Journal of Science 22/6 (December 2018), 1939-1946. https://doi.org/10.16984/saufenbilder.451646.
JAMA Büyükkütük S. Timelike Factorable Surfaces in Minkowski Space-Time. SAUJS. 2018;22:1939–1946.
MLA Büyükkütük, Sezgin. “Timelike Factorable Surfaces in Minkowski Space-Time”. Sakarya University Journal of Science, vol. 22, no. 6, 2018, pp. 1939-46, doi:10.16984/saufenbilder.451646.
Vancouver Büyükkütük S. Timelike Factorable Surfaces in Minkowski Space-Time. SAUJS. 2018;22(6):1939-46.