Geodesic
New Examples of $F$-planar Curves in 3-dimensional Warped Product Manifolds
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 2, p. 247

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The notion of $F$-planar curves generalizes the magnetic curves and implicitly the geodesics. In this note we obtain all $F$-planar curves in the Euclidean space ${\mathbb{E}}^3$ with constant coefficients and we prove that they are generalized helices. We give a detailed study for $F$-planar curves in the warped product ${\mathbb{R}}\times_f{\mathbb{R}}^2$.
Classification : 53C15, 53C25, 37J45, 37C27, 53C80
Keywords: F-planar curve, magnetic trajectory, warped product manifold 
@article{KJM_2019_43_2_a4,
     author = {Ana Irina Nistor},
     title = {New {Examples} of $F$-planar {Curves} in 3-dimensional {Warped} {Product} {Manifolds}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {247 },
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_2_a4/}
}
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Ana Irina Nistor. New Examples of $F$-planar Curves in 3-dimensional Warped Product Manifolds. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 2, p. 247 . http://geodesic.mathdoc.fr/item/KJM_2019_43_2_a4/