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http://dx.doi.org/10.5831/HMJ.2019.41.4.683

RULED SURFACES IN E3 WITH DENSITY  

Altin, Mustafa (Technical Sciences Vocational School, Bingol University)
Kazan, Ahmet (Department of Computer Technologies, Dogansehir Vahap Kucuk Vocational School of Higher Education, Malatya Turgut Ozal University)
Karadag, H.Bayram (Department of Mathematics, Faculty of Arts and Sciences, Inonu University)
Publication Information
Honam Mathematical Journal / v.41, no.4, 2019 , pp. 683-695 More about this Journal
Abstract
In the present paper, we study curves in 𝔼3 with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.
Keywords
Space with density; Weighted curvature; Ruled Surface;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 HS. Abdel-Aziz and M.K. Saad, Smarandache Curves Of Some Special Curves in the Galilean 3-Space, Honam Mathematical Journal, 37(2), (2015), 253-264.   DOI
2 A.T. Ali, Special Smarandache Curves in the Euclidean Space, Int. J. Math. Comb., 2, (2010), 30-36.
3 D. Bakry and M. Emery, Diffusions hypercontractives, Seminaire de probabilites de Strasbourg, Volume 19, (1985), 177-206.
4 H. Brauner and W. Kickinger, Baugeometrie 1, Bauverlag, (1977).
5 I. Corwin, N. Hoffman, S. Hurder, V. Sesum and Y. Xu, Differential geometry of manifolds with density, Rose-Hulman Und. Math. J., 7(1), (2006), 1-15.
6 M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Func. Anal., 13, (2003), 178-215.   DOI
7 D.T. Hieu and N.M. Hoang, Ruled minimal surfaces in $R^3$ with density $e^z$, Pac. J. Math., 243(2), (2009), 277-285.   DOI
8 D.T. Hieu and T.L. Nam, The classification of constant weighted curvature curves in the plane with a log-linear density, Commun. Pure Appl. Anal., 13(4), (2014), 1641-1652.   DOI
9 J. Hoschek, Liniengeometrie, Bibliograph. Institut, Zurich, (1971).
10 A. Kazan and H.B. Karadag, Weighted Minimal And Weighted Flat Surfaces Of Revolution In Galilean 3-Space With Density, Int. J. Anal. Appl., 16(3), (2018), 414-426.
11 F. Morgan, Manifolds with Density, Not. Amer. Math. Soc., 52(8), (2005), 853-858.
12 F. Morgan, Manifolds with Density and Perelman's Proof of the Poincare Conjecture, Am. Math. Mon., 116(2), (2009), 134-142.   DOI
13 B. O'Neill, Elementary Differential Geometry, Academic Press Inc, (1966).
14 B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, (1983).
15 B. Ravani and J.W. Wang, Computer aided geometric design of line constructs, ASME J. Mech. Des., 113(4), (1991), 363-371.   DOI
16 M. Turgut and S. Yilmaz, Smarandache Curves in Minkowski Space-time, Int. J. Math. Comb., 3, (2008), 51-55.
17 C. Rosales, A. Canete, V. Bayle and F. Morgan, On the isoperimetric problem in Euclidean space with density, Calc. Var. Partial Differ Equ., 31, (2008), 27-46.   DOI
18 J.W. Rutter, Geometry of Curves, 1st. New York: Chapman and Hall/CRC; (2000), 384.
19 S. Senyurt, Y. Altun and C. Cevahir, Smarandache curves for spherical indicatrix of the Bertrand curves pair, Boletim da Sociedade Paranaense de Matematica, 38(2), (2020), In Press, 27-39.
20 D.W. Yoon, Weighted minimal translation surfaces in Minkowski 3-space with density, Int. J. Geom. Methods Mod. Phys., 14, (2017), 175-178.
21 D.W. Yoon, D.S. Kim, Y.H. Kim and J.W. Lee, Constructions of Helicoidal Surfaces in Euclidean Space with Density, Symmetry, (2017), 9, 173.   DOI