Geodesic
Triply Orthogonal Line Congruences with Common Middle Surface
Journal for geometry and graphics, Tome 14 (2010) no. 1, pp. 45-58.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let S be a non parabolic line congruence in E3, whose middle surface P(u,v) is different from its middle envelope M(u,v). We prove that there exist two line congruences S', S'' orthogonal to S and to each other with common middle surface P(u,v) iff S is isotropic or the straight lines of S', S'' are directed by the tangent vectors of the spherical image of the S-principal ruled surfaces of S, in case S is not isotropic. Then, studying the properties of a triplet S, S', S'', we find a new geometric interpretation for the curvature of S.
Classification : 53A25
Mots-clés : Orthogonal line congruences, middle surface, middle envelope, curvature of a line congruence 
@article{JGG_2010_14_1_JGG_2010_14_1_a3,
     author = {D. Papadopoulou and P. Koltsaki },
     title = {Triply {Orthogonal} {Line} {Congruences} with {Common} {Middle} {Surface}},
     journal = {Journal for geometry and graphics},
     pages = {45--58},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a3/}
}
TY  - JOUR
AU  - D. Papadopoulou
AU  - P. Koltsaki 
TI  - Triply Orthogonal Line Congruences with Common Middle Surface
JO  - Journal for geometry and graphics
PY  - 2010
SP  - 45
EP  - 58
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a3/
ID  - JGG_2010_14_1_JGG_2010_14_1_a3
ER  - 
%0 Journal Article
%A D. Papadopoulou
%A P. Koltsaki 
%T Triply Orthogonal Line Congruences with Common Middle Surface
%J Journal for geometry and graphics
%D 2010
%P 45-58
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a3/
%F JGG_2010_14_1_JGG_2010_14_1_a3
D. Papadopoulou; P. Koltsaki . Triply Orthogonal Line Congruences with Common Middle Surface. Journal for geometry and graphics, Tome 14 (2010) no. 1, pp. 45-58. http://geodesic.mathdoc.fr/item/JGG_2010_14_1_JGG_2010_14_1_a3/