DOI QR코드

DOI QR Code

SLANT CURVES IN 3-DIMENSIONAL ALMOST f-KENMOTSU MANIFOLDS

  • Inoguchi, Jun-Ichi (Institute of Mathematics University of Tsukuba) ;
  • Lee, Ji-Eun (Research Institute for Basic Sciences Incheon National University)
  • 투고 : 2016.04.05
  • 발행 : 2017.04.30

초록

In this paper, we study slant curves in a 3-dimensional almost f-Kenmotsu manifold with proper mean curvature vector field.

키워드

참고문헌

  1. J. Arroyo, M. Barros, and O. J. Garay, A characterisation of Helices and Cornu spirals in real space forms, Bull. Austral. Math. Soc. 56 (1997), no. 1, 37-49. https://doi.org/10.1017/S0004972700030719
  2. M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1503-1509. https://doi.org/10.1090/S0002-9939-97-03692-7
  3. M. Barros and O. J. Garay, On submanifolds with harmonic mean curvature, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2545-2549. https://doi.org/10.1090/S0002-9939-1995-1254831-7
  4. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Math. 203, Birkhauser, Boston, Basel, Berlin, 2002.
  5. C. Calin and M. Crasmareanu, Slant curves in 3-dimensional normal almost contact geometry, Mediterr. J. Math. 10 (2013), no. 2, 1067-1077. https://doi.org/10.1007/s00009-012-0217-1
  6. C. Calin, M. Crasmareanu, and M.-I. Munteanu, Slant curves in three-dimensional f-Kenmotsu manifolds, J. Math. Anal. Appl. 394 (2012), no. 1, 400-407. https://doi.org/10.1016/j.jmaa.2012.04.031
  7. C. Calin and M. Ispas, On a normal contact metric manifold, Kyoungpook Math. J. 45 (2005), no. 1, 55-65.
  8. B. Y. Chen, Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), no. 2, 169-188.
  9. B. Y. Chen, Some classification theorems for submanifolds in Minkowski space-time, Arch. Math. (Basel) 62 (1994), no. 2, 177-182. https://doi.org/10.1007/BF01198672
  10. J. T. Cho, J. Inoguchi, and J.-E. Lee, On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc. 74 (2006), no. 3, 359-367. https://doi.org/10.1017/S0004972700040429
  11. J. T. Cho, J. Inoguchi, and J.-E. Lee, Biharmonic curves in 3-dimensional Sasakian space forms, Annali di Mat. Pura Appl. 186 (2007), no. 4, 685-701. https://doi.org/10.1007/s10231-006-0026-x
  12. J. Inoguchi and J.-E. Lee, Almost contact curves in normal almost contact metric 3-manifolds, J. Geom. 103 (2012), no. 3, 457-474. https://doi.org/10.1007/s00022-012-0134-2
  13. J.-E. Lee, Y. J. Suh, and H. Lee, C-parallel mean curvature vector fields along slant curves in Sasakian 3-manifolds, Kyungpook Math. J. 52 (2012), no. 1, 49-59. https://doi.org/10.5666/KMJ.2012.52.1.49
  14. Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47 (1986), no. 1, 42-50.
  15. B. O'Neill, Elementary Differential Geometry, Academic Press, 1966.
  16. V. Saltarlli, Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions, arXiv:1007.1443v4.
  17. D. J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Press Inc., Cambridge, Mass., 1950, Reprint of the second edition, Dover, New York, 1988.
  18. J. We lyczko, On Legendre curves in 3-dimensional normal almost contact metric manifolds, Soochow J. Math. 33 (2007), no. 4, 929-937.