# Slant null scrolls in Minkowski 3-space E_1^3

## Keywords:

B -scroll, null scroll, slant null scroll.## Abstract

In this study, we introduce a new type of null scrolls called slant null scrolls in Minkowski 3-space E_1^3. We define three types of slant null scrolls called alpha-slant, beta-slant and gamma-slant null scrolls and give characterizations for a null scroll to be a slant null scroll. We also give some characterizations for beta-slant B-scrolls. Moreover, for beta-slant null scrolls, we obtain some nonlinear differential equations and we give some results by using their analytical solutions. Finally, we give some examples for the obtained results.

## References

Alias, L.J., Ferrandez, A. & Lucas, P. (1994) 2-type surfaces in and . Tokyo Journal of Mathematics,

:447–454.

Alias, L.J., Ferrandez, A., Lucas, P. & Moreno, M.A. (1998) On the Gauss map of B-scrolls. Tsukuba

Journal of Mathematics, 22:371–377.

Ekici, C. & Özüsağlam, E. (2012) On the method of determination of a developable timelike ruled

surface. Kuwait Journal of Science and Engineering, 39(1A):19-41.

Ferrandez, A. & Lucas, P. (1992) On surfaces in the 3-dimensional Lorentz–Minkowski space. Pacific

Journal of Mathematics, 152:93–100.

Ferrandez, A. & Lucas, P. (2000) On the Gauss map of B-scrolls in 3-dimensional Lorentzian space

forms. Czechoslovak Mathematical Journal, 50:699–704.

Graves, L.K. (1979) Codimension one isometric immersions between Lorentz spaces. Transactions of the

American Mathematical Society, 252:367–392.

Karadağ, H.B., Kılıç, E. & Karadağ, M. (2014) On the developable ruled surfaces Kinematically

generated in Minkowski 3-Space. Kuwait Journal of Science, 41(1):21-34.

Karger, A. & Novak, J. (1978) Space Kinematics and Lie Groups, STNL Publishers of Technical Lit.

Prague, Czechoslovakia.

Kim, D.S. & Kim, Y.H. (2003) B-scrolls with non-diagonalizable shape operators. Rocky Mountain

Journal of Mathematics, 33(1):175–190.

Kim, D.S., Kim, Y.H. & Yoon, D.W. (2002) Extended B-scrolls and their Gauss maps. Indian Journal of

Pure and Applied Mathematics, 33(7):1031–1040.

Liu, H. (2004) Curves in the lightlike cone. Contributions Algebra Geometry, 45:291-303.

Liu, H. (2009a) Ruled surfaces with lightlike ruling in 3-Minkowski space. Journal of Geometry and

Physics, 59:74-78.

Liu, H. (2009b) Characterizations of Ruled Surfaces with Lightlike Ruling in Minkowski 3-space. Result

in Mathematics, 56:357–368.

Önder, M. (2013) Slant Ruled Surfaces in the Euclidean 3-space E3. arXiv:1311.0627v1 [math.DG].

Önder, M. & Kaya, O. (2015) Darboux slant ruled surfaces. Azerbaijan Journal of Mathematics, 5(1):64–

Önder, M. & Kaya, O. (2013) Characterizations of slant ruled surfaces in the Euclidean 3-space.

arxiv:1311.6928 [math.DG].