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BACKGROUND Selling of tobacco products to minors has been banned since 1996 by the tobacco control law in Turkey. However, it is also important for the public to support practices that prevent the access of tobacco products to minors. In addition, every individual has the responsibility of carrying out society based programs that restrict access to tobacco… (More)
Z. Naturforsch. 66a, 441 – 449 (2011); received June 30, 2010 / revised December 9, 2010 In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis3. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by… (More)
In this article, we study biharmonic Reeb curves in 3-dimensional Kenmotsu manifold. Moreover, we apply biharmonic Reeb curves in special 3dimensional Kenmotsu manifold K. Finally, we characterize Bertrand mate of the biharmonic Reeb curves in terms of their curvature and torsion in special 3-dimensional Kenmotsu manifold K.
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis. We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
In this paper, we study inextensible flows of focal curves associated with developable surfaces in Euclidean 3-space E3. We give some characterizations for curvature and torsion of focal curves associated with developable surfaces in Euclidean 3-space E3. Finally, we show that if flow of this developable surface is inextensible then this surface is not… (More)
In this paper, we describe a new method for constructing a tubular surface surrounding a timelike biharmonic curve in the Lorentzian Heisenberg group Heis. Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike biharmonic curves, we give explicit parametrizations of tubular surfaces in the… (More)
There are many approaches to the inextensible flows. The earliest (and most mathematically tractable), is as an equilibrium of moments, drawing on a fundamental principle of statics. Another approach, ultimately yielding the same equation for the curve, is as a minimu m of bending energy in the elastic curve. A forcebased approach finds that normal,… (More)
In this paper, biharmonic slant helices are studied according to Bishop frame in the Heisenberg group Heis. We give necessary and sufficient conditions for slant helices to be biharmonic. The biharmonic slant helices are characterized in terms of Bishop frame in the Heisenberg group Heis. We give some characterizations for tangent Bishop spherical images of… (More)
In this paper, we study inextensible flows of dual tangent developable surfaces of a curve in . 3 D Mathematics Subject Classification (2010): 53A04, 53A05.
R (X,Y ) = [∇X ,∇Y ]−∇[X,Y ], X, Y ∈ Γ (TN) . For a smooth map φ : N −→M , the Levi-Civita connection∇ of (N,h) induces a conncetion∇ on the pull-back bundle φ∗TM =p∈N Tφ(p)M. The section T (φ) := tr∇dφ is called the tension field of φ. A map φ is said to be harmonic if its tension field vanishes identically. A smooth map φ : N −→M is said to be biharmonic… (More)