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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

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 .

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.

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

Abstract

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.

Details

Primary Language English
Journal Section Research Article
Authors

Talat KORPİNAR This is me
Fırat University, Department of Mathematics, 23119, Elazı˘g, TURKEY


Essin TURHAN This is me
Fırat University, Department of Mathematics, 23119, Elazı˘g, TURKEY

Publication Date December 1, 2012
Published in Issue Year 2012, Volume 2, Issue 2

Cite

Bibtex @ { twmsjaem761709, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2012}, volume = {2}, number = {2}, pages = {178 - 184}, title = {b-m1 DEVELOPABLE SURFACES OF BIHARMONIC NEW TYPE b-SLANT HELICES ACCORDING TO BISHOP FRAME IN THE SOL SPACE Sol3}, key = {cite}, author = {Korpinar, Talat and Turhan, Essin} }