zbMATH — the first resource for mathematics

On constant slope spacelike surfaces in 3-dimensional Minkowski space. (English) Zbl 1226.53012
Summary: A space-like surface in the Minkowski 3-space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface. In this work, we study such surfaces and classify all of them.

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53A35 Non-Euclidean differential geometry
Full Text: DOI
[1] Ali, A.T.; Turgut, M., Position vector of a time-like slant helix in Minkowski 3-space, J. math. anal. appl., 365, 559-569, (2010) · Zbl 1185.53004
[2] Bilici, M.; Caliskan, M., On the involutes of the space-like curve with a time-like binormal in Minkowski 3-space, Int. math. forum, 4, 1497-1509, (2009) · Zbl 1186.53002
[3] Cermelli, P.; Di Scala, A.J., Constant-angle surfaces in liquid crystals, Philos. mag., 87, 1871-1888, (2007)
[4] Chen, B.Y., Geometry of submanifolds, (1973), Dekker New York
[5] Dillen, F.; Fastenakels, J.; Van der Veken, J.; Vrancken, L., Constant angle surfaces in \(\mathbb{S}^2 \times \mathbb{R}\), Monatsh. math., 152, 2, 89-96, (2007) · Zbl 1140.53006
[6] Dillen, F.; Munteanu, M.I., Constant angle surfaces in \(\mathbb{H}^2 \times \mathbb{R}\), Bull. braz. math. soc., 40, 1, 1-13, (2009)
[7] Fastenakels, J.; Munteanu, M.I.; Van der Veken, J., Constant angle surfaces in the Heisenberg group, Acta math. sin. (engl. ser.), 27, 4, 747-756, (2011) · Zbl 1218.53019
[8] Hano, J.; Nomizu, K., Surfaces of revolution with constant Mean curvature in Lorentz-Minkowski space, Tohoku math. J. (2), 32, 3, 427-437, (1984) · Zbl 0535.53002
[9] İlarslan, K.; Boyacıoğlu, O., Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos solitons fractals, 38, 5, 1383-1389, (2008) · Zbl 1154.53304
[10] López, R.; Munteanu, M.I., Constant angle surfaces in Minkowski space, Bull. belg. math. soc. Simon stevin, 18, 2, 271-286, (2011) · Zbl 1220.53024
[11] Munteanu, M.I., From Golden spirals to constant slope surfaces, J. math. phys., 51, 073507, (2010) · Zbl 1311.14037
[12] Munteanu, M.I.; Nistor, A.I., A new approach on constant angle surfaces in \(\mathbb{E}^3\), Turkish J. math., 33, 1, 1-10, (2009)
[13] OʼNeill, B., Semi-Riemannian geometry with applications to relativity, (1982), Academic Press New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.