Geometric Characterization of Pointwise Slant Curves
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Keywords:
Semi-Riemannian metrics, Partial differential equations, Mathematical operators, Contact structure, Slant curve, Legendre curve, LancretAbstract
In the present paper, we study the characteristics of pointwise slant curves in a normal almost contact semi-Riemannian three-manifold N3. These curves are characterized by the pseudo-Riemannian scalar product between the normal vector at the curve and the reeb vector field of manifold N3. In this class of manifolds, curvature and torsion of such curves are determined. The Lancret of slant curves in manifold N3 is obtained. Additionally, pointwise slant curves with proper mean
curvature are characterized.
References
Cho, J.T.; Inoguchi, J.; Lee, J.E. Slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 2006, 74, 359–367.
Baikoussis, C.; Blair, D.E. On Legendre curves in contact 3-manifolds. Geom. Dedicata 1994, 49, 135–142.
Calin, C.; Crasmareanu, M. Slant curves in three-dimensional normal almost contact geometry. Mediterr. J. Math. 2013, 10, 1067–1077.
Calin, C.; Crasmareanu, M.; Munteanu, M.I. Slant curves in 3-dimensional ˘ f -Kenmotsu manifolds. J. Math. Anal. Appl. 2012, 394, 400–407.
Inoguchi, J.; Lee, J.E. Slant curves in 3-dimensional almost contact metric geometry. Internat. Elect. J. Geom. 2015, 8, 106–146.
Inoguchi, J.; Lee, J.E. Almost contact curves in normal almost contact 3-manifolds. J. Geom. 2012, 103, 457–474.
Welyczko J. Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterr. J. Math. 2014, 11, 965–978.
Sood, K.; Srivastava, K.; Srivastava, S.K. PS curves in quasi-paraSasakian 3-manifolds. Mediterr. J. Math. 2020, 17, 114. https://doi.org/10.1007/s00009-020-01554-y
Blair, D.E. Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203, Birkhauser Boston, Inc. Boston, MA, 2002. ¨
Perrone, D. Contact pseudo-metric manifolds of constant curvature and CR geometry, Results Math. 2014, 66, 213–225.
Calvaruso, G.; Perrone, D. Contact pseudo-metric manifolds. Differential Geom. Appl. 2010, 28, 615–634.
Deshmukh, S.; Belova, O.; Turki, N.B.; Vˆılcu, G.E. Hypersurfaces of a Sasakian manifold-revisited. Journal of Inequalities and Applications 2021, 2021, 1-24. https://doi.org/10.1186/s13660-021-02584-0
Olszak, Z. Normal almost contact manifolds of dimension three. Ann. Pol. Math. 1986, 47, 42–50.
O’Neill, B. Semi-Riemannian geometry with applications to Relativity. Academic Press, New York, 1983.
Ali, A.T.; Turgut, M. Position vector of a time-like slant helix in Minkowski 3-space. J. Math. Anal. Appl. 2010, 365, 559–569.
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