Geodesic
On the Geodesics of Tubular Surfaces in Minkowski 3-Space
Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 1

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In this study, we research geodesics of tubular surfaces which is founded by using two-parameter spatial motion along a curve in Minkowski 3-space. To do this, we solve differential equation D T T=0 of parametric curves on the tubular surface where D is the connection of tubular surface and T is the unit vector field of two parametric curves on the tubular surface in particular. It is shown that for fixed s , all of parametric curves of the tubular surface M=φ (s,t) are geodesics and for fixed t only the curves φ {t=0} (s) are geodesics.
Classification : 53A35, 53B30. 
Murat Kemal Karacan; Yusuf Yayli. On the Geodesics of Tubular Surfaces in Minkowski 3-Space. Bulletin of the Malaysian Mathematical Society, Tome 31 (2008) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2008_31_1_a0/
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     author = {Murat Kemal Karacan and Yusuf Yayli},
     title = {On the {Geodesics} of {Tubular} {Surfaces} in {Minkowski} {3-Space}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2008},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2008_31_1_a0/}
}
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