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On slant helix and its spherical indicatrix. (English) Zbl 1083.53006

Summary: We investigate spherical images the tangent indicatrix and binormal indicatrix of a slant helix. We obtain that the spherical images are spherical helices.
Moreover, we show that a curve of constant precession is a slant helix. For involute of a curve \(\gamma\), we have obtain that \(\gamma\) is a slant helix if and only if its involute is a general helix.

MSC:

53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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References:

[1] Izumiya, S.; Tkeuchi, N., New special curves and developable surfaces, Turk. J. Math., 28, 153-163 (2004) · Zbl 1081.53003
[2] Scofield, P. D., Curves of constant precession, Am. Math. Monthly, 102, 531-537 (1995) · Zbl 0881.53002
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