Geodesic
Note on Flecnodes
Journal for geometry and graphics, Tome 13 (2009) no. 1, pp. 29-4 Cet article a éte moissonné depuis la source Heldermann Verlag

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The flecnodes Fi on a regular and non torsal ruling R0 of a ruled surface R are the points where R's asymptotic tangents along R0 hyperosculate the ruled surface. The name flecnode characterizes the intersection curve ci of the tangent plane τi with R at Fi. It has a double point (a node) at Fi and this node is an inflection point for both linear branches of ci at Fi. We show a way to parameterize the smooth one-parameter family of flecnodes of R which in general forms a curve with two branches. For that we derive the equation of the ruled quadric on three given lines in terms of Pl�cker coordinates of the given lines.
Classification : 53A05, 53A25
Mots-clés : Ruled surface, flecnode, line geometry, Lie's osculating quadric 
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     author = {B. Odehnal },
     title = {Note on {Flecnodes}},
     journal = {Journal for geometry and graphics},
     pages = {29--4},
     year = {2009},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2009_13_1_JGG_2009_13_1_a3/}
}
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B. Odehnal . Note on Flecnodes. Journal for geometry and graphics, Tome 13 (2009) no. 1, pp. 29-4. http://geodesic.mathdoc.fr/item/JGG_2009_13_1_JGG_2009_13_1_a3/