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Biharmonic spacelike curves in Lorentzian Heisenberg space

이지은
대한수학회 (The Korean Mathematical Society)|2018.10|대한수학회논문집 (Communications of the KMS)|제33권 제4호|pp. 1309-1320

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참고문헌

키워드

slant curvesbiharmonic curvesLorentzian Heisenberg space
주제분류수학

초록

In this paper, we show that proper biharmonic spacelike curve $\gamma$ in Lorentzian Heisenberg space $(\mathbb{H}_3, g)$ is pseudo-helix with \linebreak ${\kappa}^2 -{\tau}^2 = -1+4\eta(B)^2.$ Moreover, $\gamma$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

Abstract

In this paper, we show that proper biharmonic spacelike curve $\gamma$ in Lorentzian Heisenberg space $(\mathbb{H}_3, g)$ is pseudo-helix with \linebreak ${\kappa}^2 -{\tau}^2 = -1+4\eta(B)^2.$ Moreover, $\gamma$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

참고문헌 (12)

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  7. A. Ferrandez, "Riemannian Versus Lorentzian submanifolds, some open problems", proc. Workshop on Recent Topics in Differential Geometry, pp.109~130 (1998), Depto. Geom. y Topologia, Univ. Santiago de Compostera
  8. J.-I. Inoguchi, "Biharmonic curves in Minkowski 3-space", Int. J. Math. Math. Sci, (21), pp.1365~1368 (2003)
  9. G. Y. Jiang, "2-harmonic isometric immersions between Riemannian manifolds", Chinese Ann. Math. Ser. A, 7(2), pp.130~144 (1986)
  10. G. Y. Jiang, "2-harmonic maps and their first and second variational formulas", Chinese Ann. Math. Ser. A, 7(4), pp.389~402 (1986)
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  12. T. Sasahara, "Biharmonic submanifolds in non at Lorentz 3-space forms", Bull. Aust. Math. Soc, 85(3), pp.422~443 (2012)

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