Object of study in the present paper are slant and Legendre null curves in 3-dimensional Sasaki-like almost contact B-metric manifolds. For the examined curves we express the general Frenet frame and the Frenet frame for which the original parameter is distinguished, as well as the corresponding curvatures, in terms of the structure on the manifold. We prove that the curvatures of a framed null slant and Legendre curve are constants if and only if a specific function for the considered manifolds is a constant. We find a necessary and sufficient condition a slant null curve to be a generalized helix and a Legendre null curve to be a null cubic. For some of investigated curves we show that they are non-null slant or Legendre curves with respect to the associated B-metric on the manifold. We give examples of the examined curves. Some of them are constructed in a 3-dimensional Lie group as Sasaki-like manifold and their matrix representation is obtained.
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Bejan, C.L., Druta-Romaniuc, S.L.: F-geodesic on manifolds. Filomat 29(10), 2367–2379 (2015)
Duggal, K.L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic, Dordrecht (1996)
Duggal, K.L., Jin, D.H.: Null Curves and Hypersurfaces of Semi-Riemannian Manifolds. World Scientific Publishing, Singapore (2007)
Ferrandez, A., Gimenez, A., Lucas, P.: Null generalized helices in Lorentz–Minkowski spaces. J. Phys. A Math. Gen. 35, 8243–8251 (2002)
Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric. Math. Balkanica 7, 262–276 (1993)
Honda, K., Inoguchi, J.: Deformation of Cartan framed null curves preserving the torsion. Differ. Geom. Dyn. Syst. 5, 31–37 (2003)
Inoguchi, J.I.: Biharmonic curves in Minkowski 3-space. Int. J. Math. Sci. 21, 1365–1368 (2003)
Inoguchi, J.I., Lee, J.E.: On slant curves in normal almost contact metric 3-manifolds. Beitr. Algebra Geom. 55, 603–620 (2004)
Ivanov, S., Manev, H., Manev, M.: Sasaki-like almost contact complex Riemannian manifolds. J. Geom. Phys. 107, 136–148 (2016)
Manev, M.: Ph.D Thesis, Plovdiv (1998)
Welyczko, J.: Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterr. J. Math. 11, 965–978 (2014)
In memory of Professor Simeon Zamkovoy, University of Sofia, Bulgaria
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The research of S. Zamkovoy was partially supported by Contract DH/12/3/12.12.2017 and Contract 80-10-12/18.03.2020 with the Sofia University “St. Kliment Ohridski”.
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Nakova, G., Zamkovoy, S. Slant and Legendre null curves in 3-dimensional Sasaki-like almost contact B-metric manifolds. J. Geom. 112, 6 (2021). https://doi.org/10.1007/s00022-021-00571-w
- Sasaki-like almost contact B-metric manifolds
- Slant curves
- Null curves
Mathematics Subject Classification