Geodesic
C-parallel and C-proper slant curves of S-manifolds
Filomat, Tome 33 (2019) no. 19, p. 6305

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DOI

In the present paper, we define and study C-parallel and C-proper slant curves of S-manifolds. We prove that a slant curve γ in an S-manifold of order r ≥ 3, under certain conditions, is C-parallel or C-parallel in the normal bundle if and only if it is a non-Legendre slant helix or Legendre helix, respectively. Moreover, under certain conditions, we show that γ is C-proper or C-proper in the normal bundle if and only if it is a non-Legendre slant curve or Legendre curve, respectively. We also give two examples of such curves in R 2m+s (−3s)
DOI : 10.2298/FIL1919305G
Classification : 53C25, 53C40, 53A04
Keywords: C-parallel curve, C-proper curve, slant curve, S-manifold 
Şaban Güvenç; Cihan Özgür. C-parallel and C-proper slant curves of S-manifolds. Filomat, Tome 33 (2019) no. 19, p. 6305 . doi: 10.2298/FIL1919305G
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     author = {\c{S}aban G\"uven\c{c} and Cihan \"Ozg\"ur},
     title = {C-parallel and {C-proper} slant curves of {S-manifolds}},
     journal = {Filomat},
     pages = {6305 },
     year = {2019},
     volume = {33},
     number = {19},
     doi = {10.2298/FIL1919305G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1919305G/}
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