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A NEW KIND OF HELICOIDAL SURFACE OF VALUE M

Year 2014, , 154 - 162, 30.04.2014
https://doi.org/10.36890/iejg.594506

Abstract

  

References

  • [1] Baikoussis, Chr., Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature, J. Geom. 63 (1998) 25-29.
  • [2] Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J., A classification of surfaces of revolution of constant Gaussian curvature in the Minkowski space R3, Bull. Calcutta Math. Soc. 90(1998) 441-458.
  • [3] Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J., Helicoidal surfaces in three-dimensional Minkowski space, J. Math. Anal. Appl., 275 (2002) 586-614.
  • [4] Bour, E., Théorie de la déformation des surfaces. J. de l’Êcole Imperiale Polytechnique, 22-39 (1862) 1-148.
  • [5] Do Carmo, M., Dajczer, M., Helicoidal surfaces with constant mean curvature, Tohôku Math. J. 34 (1982) 351-367.
  • [6] Dillen, F., Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math. 98 (1999) 307-320.
  • [7] Eisenhart, L., A Treatise on the Differential Geometry of Curves and Surfaces, Palermo 41 Ginn and Company, 1909.
  • [8] Güler, E., Bour’s theorem and lightlike profile curve. Yokohama Math. J., 54-1 (2007) 55-77.
  • [9] Güler, E., Yaylı, Y., Hacısalihoğlu, H.H., Bour’s theorem on Gauss map in Euclidean 3-space, Hacettepe J. Math. Stat. 39-4 (2010) 515-525.
  • [10] Güler, E., Bour’s minimal surface in three dimensional Lorentz-Minkowski space, (presented in GeLoSP2013, VII International Meetings on Lorentzian Geometry, Sao Paulo University, Sao Paulo, Brasil) preprint.
  • [11] Hitt, L, Roussos, I., Computer graphics of helicoidal surfaces with constant mean curvature, An. Acad. Brasil. Ciˆenc. 63 (1991) 211-228.
  • [12] Ikawa, T., Bour’s theorem and Gauss map, Yokohama Math. J. 48-2 (2000) 173-180. [13] Ikawa, T., Bour’s theorem in Minkowski geometry, Tokyo J.Math. 24 (2001) 377-394.
  • [14] Kenmotsu, K., Surfaces of revolution with prescribed mean curvature, Tohôku Math. J. 32 (1980) 147-153.
  • [15] Spivac, M., A Comprehensive Introduction to Differential Geometry III, Interscience, New York, 1969.
  • [16] Struik, D.J., Lectures on Differential Geometry, Addison-Wesley, 1961.
Year 2014, , 154 - 162, 30.04.2014
https://doi.org/10.36890/iejg.594506

Abstract

References

  • [1] Baikoussis, Chr., Koufogiorgos, T., Helicoidal surfaces with prescribed mean or Gaussian curvature, J. Geom. 63 (1998) 25-29.
  • [2] Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J., A classification of surfaces of revolution of constant Gaussian curvature in the Minkowski space R3, Bull. Calcutta Math. Soc. 90(1998) 441-458.
  • [3] Beneki, Chr. C., Kaimakamis, G., Papantoniou, B.J., Helicoidal surfaces in three-dimensional Minkowski space, J. Math. Anal. Appl., 275 (2002) 586-614.
  • [4] Bour, E., Théorie de la déformation des surfaces. J. de l’Êcole Imperiale Polytechnique, 22-39 (1862) 1-148.
  • [5] Do Carmo, M., Dajczer, M., Helicoidal surfaces with constant mean curvature, Tohôku Math. J. 34 (1982) 351-367.
  • [6] Dillen, F., Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math. 98 (1999) 307-320.
  • [7] Eisenhart, L., A Treatise on the Differential Geometry of Curves and Surfaces, Palermo 41 Ginn and Company, 1909.
  • [8] Güler, E., Bour’s theorem and lightlike profile curve. Yokohama Math. J., 54-1 (2007) 55-77.
  • [9] Güler, E., Yaylı, Y., Hacısalihoğlu, H.H., Bour’s theorem on Gauss map in Euclidean 3-space, Hacettepe J. Math. Stat. 39-4 (2010) 515-525.
  • [10] Güler, E., Bour’s minimal surface in three dimensional Lorentz-Minkowski space, (presented in GeLoSP2013, VII International Meetings on Lorentzian Geometry, Sao Paulo University, Sao Paulo, Brasil) preprint.
  • [11] Hitt, L, Roussos, I., Computer graphics of helicoidal surfaces with constant mean curvature, An. Acad. Brasil. Ciˆenc. 63 (1991) 211-228.
  • [12] Ikawa, T., Bour’s theorem and Gauss map, Yokohama Math. J. 48-2 (2000) 173-180. [13] Ikawa, T., Bour’s theorem in Minkowski geometry, Tokyo J.Math. 24 (2001) 377-394.
  • [14] Kenmotsu, K., Surfaces of revolution with prescribed mean curvature, Tohôku Math. J. 32 (1980) 147-153.
  • [15] Spivac, M., A Comprehensive Introduction to Differential Geometry III, Interscience, New York, 1969.
  • [16] Struik, D.J., Lectures on Differential Geometry, Addison-Wesley, 1961.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Erhan Güler

Publication Date April 30, 2014
Published in Issue Year 2014

Cite

APA Güler, E. (2014). A NEW KIND OF HELICOIDAL SURFACE OF VALUE M. International Electronic Journal of Geometry, 7(1), 154-162. https://doi.org/10.36890/iejg.594506
AMA Güler E. A NEW KIND OF HELICOIDAL SURFACE OF VALUE M. Int. Electron. J. Geom. April 2014;7(1):154-162. doi:10.36890/iejg.594506
Chicago Güler, Erhan. “A NEW KIND OF HELICOIDAL SURFACE OF VALUE M”. International Electronic Journal of Geometry 7, no. 1 (April 2014): 154-62. https://doi.org/10.36890/iejg.594506.
EndNote Güler E (April 1, 2014) A NEW KIND OF HELICOIDAL SURFACE OF VALUE M. International Electronic Journal of Geometry 7 1 154–162.
IEEE E. Güler, “A NEW KIND OF HELICOIDAL SURFACE OF VALUE M”, Int. Electron. J. Geom., vol. 7, no. 1, pp. 154–162, 2014, doi: 10.36890/iejg.594506.
ISNAD Güler, Erhan. “A NEW KIND OF HELICOIDAL SURFACE OF VALUE M”. International Electronic Journal of Geometry 7/1 (April 2014), 154-162. https://doi.org/10.36890/iejg.594506.
JAMA Güler E. A NEW KIND OF HELICOIDAL SURFACE OF VALUE M. Int. Electron. J. Geom. 2014;7:154–162.
MLA Güler, Erhan. “A NEW KIND OF HELICOIDAL SURFACE OF VALUE M”. International Electronic Journal of Geometry, vol. 7, no. 1, 2014, pp. 154-62, doi:10.36890/iejg.594506.
Vancouver Güler E. A NEW KIND OF HELICOIDAL SURFACE OF VALUE M. Int. Electron. J. Geom. 2014;7(1):154-62.