Geodesic
Normal congruence of paraboloid. Demiquadrics
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2015), pp. 5-19

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It is an important problem to build a family of lines on the paraboloid of rotation with certain properties convenient for metallic mesh tailoring upon designing and manufacturing a parabolic antenna. Namely, the lines of this family should be locally close to geodesic lines to a reasonable extent, and an algorithm relating the line of this family to the natural parameter is also necessary. The first and important step has been made in solving the problem: a class of surfaces whose intersection with the paraboloid generates a class of lines promising for the achievement of the declared goals is revealed. These surfaces are demiquadrics associated in a special way with the normal congruence of the paraboloid.
Mots-clés : paraboloid, antenna, demiquadrics.
Keywords: geodesic line, normal congruence 
@article{VTGU_2015_5_a0,
     author = {M. S. Bukhtyak},
     title = {Normal congruence of paraboloid. {Demiquadrics}},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--19},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2015_5_a0/}
}
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M. S. Bukhtyak. Normal congruence of paraboloid. Demiquadrics. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2015), pp. 5-19. http://geodesic.mathdoc.fr/item/VTGU_2015_5_a0/