A new approach for describing instantaneous line congruence

Abdel-Baky, Rashad A.   ; Al-Bokhary, Ashwaq J.

Archivum mathematicum, Tome 44 (2008) no. 3, pp. 223-236

Abstract (VO)

Based on the E. Study’s map, a new approach describing instantaneous line congruence during the motion of the Darboux frame on a regular non-spherical and non-developable surface, whose parametric curves are lines of curvature, is proposed. Afterward, the pitch of general line congruence is developed and used for deriving necessary and sufficient condition for instantaneous line congruence to be normal. In terms of this, the derived line congruences and their differential geometric invariants were examined.

Détail

Classification : 53A04, 53A05, 53A17
Keywords: lines of curvature; line congruence; E. Study’s map; instantaneous revolution axis

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