A NEW KIND OF HELICOIDAL SURFACE OF VALUE M

Year 2014, Volume: 7 Issue: 1, 154 - 162, 30.04.2014

Erhan Güler

https://doi.org/10.36890/iejg.594506

Cited By: 4

Abstract

  

Keywords

Helicoidal surface of value m, rotational surface of value m, mean curvature, Gaussian curvature, Gauss map

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.