2015
DOI: 10.1007/s00006-015-0610-5
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General Helices with Timelike Slope Axis in Minkowski 3-Space

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Cited by 9 publications
(7 citation statements)
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“…Substituting (19) in the first equation of (18), we obtain that the curvature functions of α satisfy the relation k e − τ ds k n e τ ds ds + k n e τ ds k e − τ ds ds = 0.…”
Section: Proposition 32mentioning
confidence: 99%
“…Substituting (19) in the first equation of (18), we obtain that the curvature functions of α satisfy the relation k e − τ ds k n e τ ds ds + k n e τ ds k e − τ ds ds = 0.…”
Section: Proposition 32mentioning
confidence: 99%
“…Substituting (17) in the first equation of (16), we obtain that the geodesic curvature satisfies the differential equation k ′′ g − k g k ′ g = 0. Solving the above second-order differential equation, we get the next theorem.…”
Section: Theoremmentioning
confidence: 99%
“…10 For the recent characterizations of the general and slant helices, we refer to previous studies. [12][13][14][15][16][17] Isophotic curves in E 3 are the regular curves that lie on a surface and have a property that the surface normals along those curves make a constant angle with a fixed direction. Isophotic curves are related with general and slant helices as follows: Geodesic isophotic curves are slant helices, and asymptotic isophotic curves are general helices.…”
Section: Introductionmentioning
confidence: 99%
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“…These are geodesics of cylinders shaped over a plane curve. Recently, general helices with different slope axis were investigated in [5,18,19]. Slant helices are the successor curves of the general helices [15].…”
Section: Introductionmentioning
confidence: 99%