TY  - JOUR
TI  - WñLINE CONGRUENCES
AB  - By utilizing the Darboux frames, along with a regular surface whose parametric curves are lines of curvature, we analyzed the normal line congruence which preserves the asymptotic curves between its focal surfaces. This allows deriving systems of partial di§erential equations through which the problem of determining the director surface and the corresponding normal line congruence could be solved. Moreover, a necessary and su¢ cient condition that the focal surfaces of the normal line congruence are degenerates into curves is derived. As a result the middle focal surface of the normal line congruence is presented as a new surface interrogation tool.
AU  - abdel-baky, rashadd
AU  - TAS, FERHAT
DO  - 10.31801/cfsuasmas.550369
PY  - 2020
JO  - Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
VL  - 69
IS  - 1
SN  - 1303-5991
SP  - 450
EP  - 460
DB  - TRDizin
UR  - http://search/yayin/detay/1204293
ER  -