N-Legendre and N-slant curves in the unit tangent bundle of surfaces

Authors

  • Fouzi Hathout Saida University
  • Murat Bekar Necmettin Erbakan University
  • Yusuf Yayli Ankara University

Keywords:

Unit tangent bundle, Sasaki metric, N-legendre, N-slant and Sectional curvature

Abstract

Let (T1M; g1) be a unit tangent bundle of some surface (M; g) en-dowed with the induced Sasaki metric. In this present paper, we de-ne two kinds of curves called N-legendre and N-slant curves as curveshaving an inner product of normal vector and Reeb vector zero andnonzero constant respectively and several important characterizationsof these curves are obtained.

References

Blair D.E. Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, Mass, USA, vol. 203 of Progress in Mathematics, 2002.

C¼alin C, Crasmareanu M. Slant curves in 3-dimensional normal almost contact geometry. Mediterranean Journal of Mathematics 2013; 10: 1067-1077.

Cho J.T, Inoguchi J.I, Lee J.E. On slant curves in Sasakian 3 manifolds. Bulletin of the Australian Mathematical Society 2006; 74: 359-367.

Fukunaga T, Takahashi M. Evolutes and involutes of frontals in the Euclidean plane. Demonstratio mathematica 2015; 48: 1-20.

Hathout F, Dida H.M. Diagonal lift in the tangent bundle of order two and its applications. Turk J Math 2006; 30: 373 384.

Janssens D, Vanhecke L. Almost contact structures and curvature tensors. Kodai Mathematical Journal 1981; 4: 1-27.

Sasaki S. On the di¤erential geometry of tangent bundles of Riemannian manifolds. The Tohoku Mathematical Journal 1962; 14: 146-155.

Tashiro Y. On contact structure of hypersurfaces in complex manifolds. The Tohoku Mathematical Journal 1963; 15: 62-78.

Zhong H.H, Lei S. Slant Curves in the Unit Tangent Bundles of Surfaces. Hindawi publishing corporation ISRN geometry 2013; 2013: 1-5.

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Published

21-07-2017