???+?? Yoğunluklu ?? Uzayında Sıfır Ağırlıklı Eğriliğe Sahip Null Olmayan Düzlemsel Eğrilerin Oluşturduğu Yüzeyler

Bu çalışmada, ???+?? yoğunluklu ?3 Lorentz-Minkowski uzayında, ikisi aynı anda sıfır olmayan ? ve ? sabitlerinin durumlarına göre, ağırlıklı eğrilikleri sıfır olan spacelike ve timelike düzlemsel eğriler yardımıyla oluşturulan dönel yüzeyler ve regle yüzeyler çalışılmıştır.

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

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 ?3 with density ???+?? according to the cases of not all zero constants ? and ? are studied.

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  • 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.
  • Albujer, A.L. and Caballero, M. 2017. “Geometric Properties of Surfaces with the Same Mean Curvature in ?3 and L3”, J. Math. Anal. Appl., 445, 1013-1024.
  • Ali, A.T. 2010. “Special Smarandache Curves in the Euclidean Space”, Int. J. Math. Comb., 2, 30-36.
  • Ali, A.T. 2012. “Position Vectors of curves in the Galilean Space ?3”, Matematnykn Bechnk, 64(3), 200–210.
  • Altın, M., Kazan, A. and Karadağ, H.B. 2019a. “Rotational Surfaces Generated by Planar Curves in ?3 with Density”, Int. J. Anal. Appl., 17(3), 311-328.
  • Altın, M., Kazan, A. and Karadağ, H.B. 2019b. “Ruled Surfaces in ?3 with Density”, Honam Mathematical Journal, 41(4), 683- 695.
  • Altın, M., Kazan, A. and Karadağ, H.B. 2020. “Monge Hypersurfaces in Euclidean 4-Space with Density”, Journal of Polytechnic, 23(1): 207-214.
  • Baikoussis, C. and Blair, D.E. 1992. “On the Gauss map of ruled surfaces”, Glasgow Math. J., 34, 355-359.
  • Belarbi, L. and Belkhelfa, M. 2012. “Surfaces in ?3 with Density”, i-manager's Journal on Mathematics, 1(1), 34-48.
  • Choi, J.H., Kim, Y.H. and Ali, A.T. 2012. “Some associated curves of Frenet non- lightlike curves in ?3”, J. Math. Anal. Appl., 394, 712–723.
  • 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.
  • Dillen, F., Pas, J. and Verstraelen, L. 1990. “On the Gauss map of surfaces of revolution”, Bull. Inst. Math. Acad. Sinica, 18, 239-246.
  • Dillen, F. and Kühnel, W. 1999. “Ruled Weingarten surfaces in Minkowski 3-space”, Manuscripta Math., 98, 307–320. Divjak, B. 1998. “Curves in Pseudo-Galilean Geometry”, Annales Univ. Sci. Budapest., 41, 117-128.
  • Ekici, C. and Öztürk, H. 2013. “On Time-Like Ruled Surfaces in Minkowski 3-Space”, Universal Journal of Applied Science, 1(2), 56-63.
  • Gromov, M. 2003. “Isoperimetry of waists and concentration of maps”, Geom. Func. Anal., 13, 178-215.
  • 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.
  • 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.
  • 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.
  • López, R. 2014. “Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space”, Int. Electron. J. Geom., 1, 44–107.
  • Morgan, F. 2005. “Manifolds with Density”, Not. Amer. Math. Soc., 52(8) ,853-858.
  • Morgan, F. 2006. “Myers' Theorem With Density”, Kodai Math. J., 29, 455-461.
  • Nam, T.L. 2017. “Some results on curves in the plane with log-linear density”, Asian- European J. of Math., 10(2), 1-8.
  • 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.
  • Turgut, A. and Hacısalihog˘lu, H.H. 1998. “Timelike Ruled Surfaces in the Minkowski 3-Space-II”, Turk. J. of Math., 22, 33-46.
  • Turgut, M. and Yilmaz, S. 2008. “Smarandache Curves in Minkowski Space- time”, Int. J. Math. Comb., 3, 51-55.
  • 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.
  • Yoon, D.W. 2017. “Weighted Minimal Translation Surfaces in Minkowski 3-space with Density”, Int. J. Geom. Methods Mod. Phys., 14(12), 1-10.
  • 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).