Abstract
The present paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non-Frenet slant curves (with null tangents or null normals) are studied. We illustrate such results by some examples.
Article PDF
Similar content being viewed by others
References
Belkhelfa M., Hiricǎ I.E., Rosa R., Verstraelen L.: On Legendre curves in Riemannian and Lorentzian Sasaki spaces. Soochow J. Math. 28(1), 81–91 (2002)
Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds, vol. 203. Springer, Berlin (2010)
Bonnor, W.B.: Curves with null normals in Minkowski space-time. In: Vaidya, E.H.P.C., RaychaudhuriA, A.K.(eds.) Random walk in relativity and cosmology. Wiley Easten Limited, New Delhi, pp. 33–47 (1985)
Cappelletti Montano B.: Bi-Legendrian structures and paracontact geometry. Int. J. Geom. Meth. Mod. Phys. 6, 487–504 (2009)
Cǎlin, C., Crasmareanu, M.: Slant Curves in 3-dimensional Normal Almost Contact Geometry. Mediterr. J. Math. 10(2), 1067–1077 (2013)
Cǎlin, C., Crasmareanu, M.: Slant curves and particles in 3-dimensional warped products and their Lancret invariants. Bull. Austr. Math. Soc. Available on CJO2012. (2004). doi:10.1017/S0004972712000809
Cǎlin C., Crasmareanu M., Munteanu M.: Slant curves in 3-dimensional f -Kenmotsu manifolds. J. Math. Anal. Appl. 394, 400–407 (2012)
Cho J.T., Inoguchi J.I., Lee J.E.: On slant curves in Sasakian space forms. J. Korean Math. Soc. 74(3), 359–367 (2006)
Cho J.T., Lee J.E.: Slant curves in contact pseudo-Hermitian 3-manifolds. Bull. Aust. Math. Soc. 78(3), 383–396 (2008)
Dacko, P.: On almost para-cosymplectic manifolds. Tsukuba J. Math. 28(1):193–213 (2004)
Duggal, K.L.: A Report on Canonical Null Curves and Screen Distributions for Lightlike Geometry. Acta Appl. Math. 95:135–149 (2007)
Duggal, K.L., Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications. Mathematics and its Applications, vol. 364. Kluwer Academic Publishers Group, Dordrecht (1996)
Duggal, K.L., Jin, D.H.: Null curves and hypersurfaces of semi-Riemannian manifolds. World Scientific Publishing, Singapore (2007)
Erdem S.: On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ,φ′)-holomorphic maps between them. Houston J. Math. 28, 21–45 (2002)
Fetcu D.: Biharmonic Legendre curves in sasakian space forms. J. Korean Math. Soc. 45(2), 393–404 (2008)
Graves, L.K.: Codimension one isometric immersions between Lorentz spaces. Trans. Am. Math.Soc. 252, 367–392 (1979)
Ilarslan K., Nešović E.: Timelike and null normal curves in Minkowski space \({{\mathbb E}^3_1}\) . Indian J. Pure Appl. Math. 35(7), 881–888 (2004)
Inoguchi, J.I.: Biharmonic curves in Minkowski 3-space. II. Int. J. Math. Math. Sci. 2006, 1–4 (2006)
Kocayigit, H., Hacisalihoglu, H.H.: 1-type and biharmonic frenet curves in Lorentzian 3-space. Iranian J. Sci. Technol. Trans. A Sci. 33, 159–168 (2009)
Kaneyuki S., Williams F.L.: Almost paracontact and paraHodge structures on manifolds. Nagoya Math. J. 99, 173–187 (1985)
Lee, H.: On Legendre curves in contact pseudo-Hermitian 3-manifolds. Bull. Aust. Math. Soc. 81(1):156–164 (2010)
Wełyczko J.: On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Results Math. 54, 377–387 (2009)
Zamkovoy S.: Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36(1), 37–60 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Wełyczko, J. Slant Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds. Mediterr. J. Math. 11, 965–978 (2014). https://doi.org/10.1007/s00009-013-0361-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-013-0361-2