Abstract and Applied Analysis

A New Approach on Helices in Pseudo-Riemannian Manifolds

Evren Zıplar, Yusuf Yaylı, and İsmail Gök

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A proper curve α in the n -dimensional pseudo-Riemannian manifold ( M , g ) is called a V n -slant helix if the function g ( V n , X ) is a nonzero constant along α , where X is a  parallel vector field along α and V n is n th Frenet frame. In this work, we study such curves and give important characterizations about them.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 718726, 6 pages.

First available in Project Euclid: 2 October 2014

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Zıplar, Evren; Yaylı, Yusuf; Gök, İsmail. A New Approach on Helices in Pseudo-Riemannian Manifolds. Abstr. Appl. Anal. 2014 (2014), Article ID 718726, 6 pages. doi:10.1155/2014/718726. https://projecteuclid.org/euclid.aaa/1412273253

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  • A. Jain, G. Wang, and K. M. Vasquez, “DNA triple helices: biological consequences and therapeutic potential,” Biochimie, vol. 90, no. 8, pp. 1117–1130, 2008.
  • Y. Yin, T. Zhang, F. Yang, and X. Qiu, “Geometric conditions for fractal super carbon nanotubes with strict self-similarities,” Chaos, Solitons and Fractals, vol. 37, no. 5, pp. 1257–1266, 2008.
  • G. Scarr, “Helical tensegrity as a structural mechanism in human anatomy,” International Journal of Osteopathic Medicine, vol. 14, no. 1, pp. 24–32, 2011.
  • M. A. Lancret, “Memoire sur les courbes a double courbure,” Mémoires Présentés à l'Institut, vol. 1, pp. 416–454, 1806.
  • D. J. Struik, Lectures on Classical Differential Geometry, Dover, New York, NY, USA, 1988.
  • E. Özdamar and H. H. Hacisalihoğlu, “A characterization of inclined curves in Euclidean $n$-space,” Communications de la Faculté des Sciences de l'Université d'Ankara. Series A1, vol. 24, no. 3, pp. 15–22, 1975.
  • S. Izumiya and N. Takeuchi, “New special curves and developable surfaces,” Turkish Journal of Mathematics, vol. 28, no. 2, pp. 531–537, 2004.
  • M. Önder, M. Kazaz, H. Kocayiğit, and O. Kiliç, “${B}_{2}$-slant helix in Euclidean 4-space ${E}^{4}$,” International Journal of Contemporary Mathematical Sciences, vol. 3, no. 29–32, pp. 1433–1440, 2008.
  • \.I. Gök, Ç. Camci, and H. H. Hacisalihoğlu, “${V}_{n}$-slant helices in Euclidean $n$-space ${E}^{n}$,” Mathematical Communications, vol. 14, no. 2, pp. 317–329, 2009.
  • \.I. Gök, Ç. Camc\i, and H. H. Hac\isalihoğlu, “${V}_{n}$-slant helices in Minkowski $n$-space ${E}_{1}^{n}$,” Communications de la Faculté des Sciences de l'Université d'Ankara. Séries A1, vol. 58, no. 1, pp. 29–38, 2009.
  • A. T. Ali and R. López, “Some characterizations of inclined curves in Euclidean ${E}^{n}$ space,” Novi Sad Journal of Mathematics, vol. 40, no. 1, pp. 9–17, 2010.
  • A. T. Ali and M. Turgut, “Some characterizations of slant helices in the Euclidean space ${E}^{n}$,” Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 3, pp. 327–336, 2010.
  • M. Külahc\i, M. Bektaş, and M. Ergüt, “On harmonic curvatures of a Frenet curve in Lorentzian space,” Chaos, Solitons and Fractals, vol. 41, no. 4, pp. 1668–1675, 2009.
  • S. Özkald\i, \.I. Gök, Y. Yayl\i, and H. H. Hacisalihoğlu, “LC slant helix on hypersurfaces in Minkowski space ${E}_{1}^{n+1}$,” TWMS Journal of Pure and Applied Mathematics, vol. 1, no. 2, pp. 137–145, 2010.
  • Ç. Camc\i, K. \.Ilarslan, L. Kula, and H. H. Hac\isalihoğlu, “Harmonic curvatures and generalized helices in ${E}^{n}$,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2590–2596, 2009.
  • A. Şenol, E. Ziplar, Y. Yayli, and \.I. Gök, “A new approach on helices in Euclidean $n$-space,” Mathematical Communications, vol. 18, no. 1, pp. 241–256, 2013.
  • B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, NY, USA, 1983.
  • H. H. Song, “On proper helices in pseudo-Riemannian submanifolds,” Journal of Geometry, vol. 91, no. 1-2, pp. 150–168, 2008. \endinput