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A new approach for describing instantaneous line congruence

Rashad A. Abdel-BakyAshwaq J. Al-Bokhary — 2008

Archivum Mathematicum

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...

Ruled W-surfaces in Minkowski 3-space 1 3

Rashad A. Abdel-BakyH. N. Abd-Ellah — 2008

Archivum Mathematicum

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set { K , K I I , H , H I I } , where ( K , H ) and ( K I I , H I I ) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

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