On Bishop frame of a null Cartan curve in Minkowski space-time
2018 ◽
Vol 15
(08)
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pp. 1850142
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Keyword(s):
In this paper, we define the Bishop frame of a null Cartan curve in Minkowski space-time [Formula: see text]. We obtain the Bishop’s frame equations of a null Cartan curve which lies in the timelike hyperplane of [Formula: see text]. We show that a null Cartan cubic lying in the timelike hyperplane of [Formula: see text] has two Bishop frames, one of which coincides with its Cartan frame. We also derive the Bishop’s frame equation of the null Cartan curve which has the third Cartan curvature [Formula: see text]. As an application, we find a solution of the null Betchov-Da Rios vortex filament equation in terms of a null Cartan curve and its Bishop frame, which generates a timelike Hasimoto surface.
2017 ◽
Vol 3
(4)
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pp. 3575-3591
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2016 ◽
Vol 46
(1)
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pp. 159-170
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2007 ◽
Vol 16
(06)
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pp. 1027-1041
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2010 ◽
Vol 07
(02)
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pp. 185-213
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2015 ◽
Vol 93
(10)
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pp. 1005-1008
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2011 ◽
Vol 2011
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pp. 1-19
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2015 ◽
Vol 30
(03)
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pp. 1550019
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