e^(ax+by) Yoğunluklu E^3_1 Uzayında Sıfır Ağırlıklı Eğriliğe Sahip Null Olmayan Düzlemsel Eğrilerin Oluşturduğu Yüzeyler

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 45 - 55, 28.02.2020

Mustafa Altın , Ahmet Kazan , H.bayram Karadağ

https://doi.org/10.18185/erzifbed.601728

Abstract

Bu çalışmada, e^(ax+by) yoğunluklu E^3_1  Lorentz-Minkowski uzayında, ikisi aynı anda sıfır olmayan a ve b sabitlerinin durumlarına göre, ağırlıklı eğrilikleri sıfır olan spacelike ve timelike düzlemsel eğriler yardımıyla oluşturulan dönel yüzeyler ve regle yüzeyler çalışılmıştır.

Keywords

Ağırlıklı eğrilik, yoğunluklu Lorentz-Minkowski uzayı, spacelike eğri, timelike eğri, dönel yüzey, regle yüzey

Supporting Institution

İnönü Üniversitesi BAP Birimi

Project Number

FDK-2018-1349

Thanks

İnönü Üniversitesi BAP Birimine desteklerinden dolayı teşekkür ederiz.

Surfaces Constructed by Non-Null Planar Curves with Vanishing Weighted Curvature in 𝑬𝟏𝟑 with Density 𝒆𝒂𝒙+𝒃𝒚

Abstract

In the present paper, the surfaces of revolution and ruled surfaces which are constructed with the aid of spacelike and timelike planar curves with vanishing weighted curvatures in Lorentz-Minkowski space 𝐸13 with density 𝑒𝑎𝑥+𝑏𝑦 according to the cases of not all zero constants 𝑎 and 𝑏 are studied.

Keywords

Weighted curvature, Lorentz-Minkowski space with density, spacelike curve, timelike curve, surface of revolution, ruled surface.

Project Number

FDK-2018-1349

References

• [1] Abdel-Aziz, H.S. and Saad, M.K., 2015, “Smarandache Curves of Some Special Curves in the Galilean 3-Space”, Honam Mathematical Journal, 37(2), 253-264.
• [2] Albujer, A.L. and Caballero, M., 2017, “Geometric Properties of Surfaces with the Same Mean Curvature in R^3 and L^3”, J. Math. Anal. Appl., 445, 1013-1024.
• [3] Ali, A.T., 2010, “Special Smarandache Curves in the Euclidean Space”, Int. J. Math. Comb., 2, 30-36.
• [4] Ali, A.T., 2012, “Position Vectors of curves in the Galilean Space G_3”, Matematnykn Bechnk, 64(3), 200–210.
• [5] Baikoussis, C. and Blair, D.E., 1992, “On the Gauss map of ruled surfaces”, Glasgow Math. J., 34, 355-359.
• [6] Belarbi, L. and Belkhelfa, M., 2012, “Surfaces in R^3 with Density”, i-manager’s Journal on Mathematics, 1(1), 34-48.
• [7] Choi, J.H., Kim, Y.H. and Ali, A.T., 2012, “Some associated curves of Frenet non-lightlike curves in E_1^3”, J. Math. Anal. Appl., 394, 712–723.
• [8] Corwin, I., Hoffman, N., Hurder, S., Sesum, V. and Xu, Y., 2006, “Differential geometry of manifolds with density”, Rose-Hulman Und. Math. J., 7(1), 1-15.
• [9] Dillen, F., Pas, J. and Verstraelen, L., “On the Gauss map of surfaces of revolution”, Bull. Inst. Math. Acad. Sinica, 18, 239-246.
• [10] Dillen, F. and Kühnel, W., 1999, “Ruled Weingarten surfaces in Minkowski 3-space”, Manuscripta Math., 98, 307–320.
• [11] Divjak, B., 1998, “Curves in Pseudo-Galilean Geometry”, Annales Univ. Sci. Budapest., 41, 117-128.
• [12] Ekici, C. and Öztürk, H., 2013, “On Time-Like Ruled Surfaces in Minkowski 3-Space”, Universal Journal of Applied Science, 1(2), 56-63.
• [13] Gromov, M., 2003, “Isoperimetry of waists and concentration of maps”, Geom. Func. Anal., 13, 178-215.
• [14] Hieu, D.T. and Nam, T.L., 2013, “The classification of constant weighted curvature curves in the plane with a log-linear density”, Commun. Pure Appl. Anal., 13, 1641-1652.
• [15] Kazan, A. and Karadağ, H.B., 2011, “A Classification of Surfaces of Revolution in Lorentz-Minkowski Space”, Int. J. Contemp. Math. Sciences, Vol. 6, no. 39, 1915-1928.
• [16] Kazan, A. and Karadağ, H.B., 2018, “Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density”, Int. J. Anal. Appl., 16(3), 414-426.
• [17] López, R., 2014, “Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space”, Int. Electron. J. Geom., 1, 44–107.
• [18] Morgan, F., 2005, “Manifolds with Density”, Not. Amer. Math. Soc., 52(8) ,853-858.
• [19] Morgan, F., 2006, “Myers’ Theorem With Density”, Kodai Math. J., 29, 455-461.
• [20] Nam, T.L., 2017, “Some results on curves in the plane with log-linear density”, Asian-European J. of Math., 10(2), 1-8.
• [21] Şenyurt, S., Altun, Y. and Cevahir, C., 2020, “Smarandache curves for spherical indicatrix of the Bertrand curves pair”, Boletim da Sociedade Paranaense de Matematica, 38(2), In Press, 27-39.
• [22] Turgut, A. and Hacısalihog ̆lu, H.H., 1998, “Timelike Ruled Surfaces in the Minkowski 3-Space-II”, Turk. J. of Math., 22, 33-46.
• [23] Turgut, M. and Yilmaz, S., 2008, “Smarandache Curves in Minkowski Space-time”, Int. J. Math. Comb., 3, 51-55.
• [24] Yoon, D.W., Kim, D-S., Kim, Y.H. and Lee, J.W., 2017, “Constructions of Helicoidal Surfaces in Euclidean Space with Density”, Symmetry, 173, 1-9.
• [25] Yoon, D.W., 2017, “Weighted Minimal Translation Surfaces in Minkowski 3-space with Density”, Int. J. Geom. Methods Mod. Phys.,, 14(12), 1-10.
• [26] Yoon, D.W. and Yüzbaşı, Z.K., 2018, “Weighted Minimal Affine Translation Surfaces in Euclidean Space with Density”, Int. J. Geom. Methods Mod. Phys., 15(11).