b-m1 DEVELOPABLE SURFACES OF BIHARMONIC NEW TYPE b-SLANT HELICES ACCORDING TO BISHOP FRAME IN THE SOL SPACE Sol3

Year 2012, Volume: 2 Issue: 2, 178 - 184, 01.12.2012

Talat Korpinar Essin Turhan

Abstract

In this paper, we study b−m1 developable surfaces of biharmonic new type b−slant helix in the Sol3 . We characterize the b−m1 developable surfaces in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol3 .

Keywords

New type b−slant helix, Sol space, curvatures, b−m1developable surface

References

• Bishop, L. R., (1975), There is More Than One Way to Frame a Curve, Amer. Math. Monthly, 82(3), 251.
• Bodduluri, R. M. C. and Ravani, B., (1992), Geometric design and fabrication of developable surfaces
• ASME Adv. Design Autom., 2, 243-250. Dillen, F. and Kuhnel, W., (1999), Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320.
• Dimitric, I., (1992), Submanifolds ofEmwith harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica, 20, 53-65.
• Eells, J. and Lemaire, L., (1978), A report on harmonic maps, Bull. London Math. Soc., 10, 1-68.
• Eells, J. and Sampson, J. H., (1964), Harmonic mappings of Riemannian manifolds, Amer. J. Math., , 109-160.
• Jiang, G. Y., (1986), 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A, 7(2), 130-144.
• K¨orpınar, T. and Turhan, E., Biharmonic new type b-slant helices according to Bishop frame in the sol space, submitted. Lancret, M. A., (1806), Memoire sur les courbes ‘a double courbure, Memoires presentes alInstitut, , 416-454. Loubeau, E. and Montaldo, S., (2004)
• Biminimal immersions in space forms, preprint, math.DG/0405320 v1.
• Ou, Y. and Wang, Z., (2008), Linear Biharmonic Maps into Sol, Nil and Heisenberg Spaces, Mediterr. J. Math., 5, 379-394.
• Rahmani, S., (1992), Metriqus de Lorentz sur les groupes de Lie unimodulaires, de dimension trois
• Journal of Geometry and Physics, 9, 295-302. Sun, M. and Fiume, E., (1996), A technique for constructing developable surfaces, In Proceedings of Graphics Interface.
• Turhan, E. and K¨orpınar, T., (2010), On Characterization Of Timelike Horizontal Biharmonic Curves
• In The Lorentzian Heisenberg Group Heis3, Zeitschrift f¨ur Naturforschung A- A Journal of Physical Sciences, 65a, 641-648. Turhan, E. and K¨orpınar, T., (2013), Parametric equations of general helices in the sol space Sol3
• Bol. Soc. Paran. Mat., 31(1), 99-104. Talat K¨orpınar and Essin Turhan, for photographs and biographies, see TWMS Jour- nal of Applied and Engineering Mathematics, Volume 2, No.1, 2012.