Abstract
In this paper, B-tubular surfaces in terms of biharmonic spacelike new type B-slant helices according to Bishop frame in the Lorentzian Heisenberg group H3 are studied. The Necessary and sufficient conditions for new type B-slant helices to be biharmonic are obtained. B-tubular surfaces in the cLorentzian Heisenberg group H3 are characterized. Additionally, main results in Figures 1, 2, 3 and 4 are illustrated.
Highlights
Tubular surfaces are very useful for representing long thin objects, for instance, poles, 3D fonts, brass instrument or internal organs of the body in solid modeling
Canal surfaces are among the surfaces which are easier to describe both analytically and operationally, (CARMO, 1976), (O'NEIL, 1983), (FAROUKI; NEFF, 1990), (LU, 1994), (GRAY, 1998), (PETERNELL; POTTMANN, 1997), (ZHU et al, 2005), (XU et al, 2006), (KORPINAR; TURHAN, 2011), (TURHAN; KORPINAR, 2011a)
If is a space curve, a tubular surface associated to this curve is a surface swept by a family of spheres of constant radius, having the center on the given curve
Summary
Tubular surfaces are very useful for representing long thin objects, for instance, poles, 3D fonts, brass instrument or internal organs of the body in solid modeling. The aim of this paper is to study tubular surfaces surrounding biharmonic spacelike B slant helices according to Bishop frame in the Lorentzian Heisenberg group H3. We study B tubular surfaces in terms of biharmonic spacelike new type B -slant helices according to Bishop frame in the Lorentzian Heisenberg group H3. To separate a spacelike new type slant helix according to Bishop frame from that of FrenetSerret frame, in the rest of the paper, we shall use notation for the curve defined above as spacelike new type B-slant helix. Assume that the center curve of B tubular surface MB s, t is a unit speed spacelike biharmonic B slant helix and MB denote a patch that parametrizes the envelope of the spheres defining the tubular surface.
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