Construction of inverse curves of general helices in the Sol space Sol³
Abstract
In this paper, we study inverse curves of general helices in the Sol³. Finally, we find out explicit parametric equations of inverse curves in the Sol³.
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References
A. Gray, Modern differential geometry of curves and surfaces with mathematica. CRC Press LLC, (1998).
G. Y. Jiang, 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A 7(2), 130-144, (1986).
T. Korpınar and E. Turhan, On Spacelike Biharmonic Slant Helices According to Bishop Frame in the Lorentzian Group of Rigid Motions E(1, 1), Bol. Soc. Paran. Mat. 30 (2), 91-100, (2012). https://doi.org/10.5269/bspm.v30i2.14558
M. A. Lancret: Memoire sur les courbes a double courbure, Memoires presentes al Institut 1, 416-454, (1806).
E. Loubeau and S. Montaldo, Biminimal immersions in space forms, preprint, 2004, math.DG/0405320 v1.
Y. Ou and Z. Wang, Linear Biharmonic Maps into Sol, Nil and Heisenberg Spaces, Mediterr. j. math. 5, 379-394, (2008). https://doi.org/10.1007/s00009-008-0157-y
D. J. Struik, Lectures on Classical Differential Geometry, Dover, New-York, (1988).
E. Turhan and T. Korpınar, Parametric equations of general helices in the sol space Sol3 , Bol. Soc. Paran. Mat. 31 (1), 99-104, (2013). https://doi.org/10.5269/bspm.v31i1.15331
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