A new approach for describing instantaneous line congruence

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

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 3, page 223-236
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Abdel-Baky, Rashad A., and Al-Bokhary, Ashwaq J.. "A new approach for describing instantaneous line congruence." Archivum Mathematicum 044.3 (2008): 223-236. <http://eudml.org/doc/250499>.

@article{Abdel2008,
abstract = {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.},
author = {Abdel-Baky, Rashad A., Al-Bokhary, Ashwaq J.},
journal = {Archivum Mathematicum},
keywords = {lines of curvature; line congruence; E. Study’s map; instantaneous revolution axis; lines of curvature; line congruence; E. Study's map; instantaneous revolution axis},
language = {eng},
number = {3},
pages = {223-236},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A new approach for describing instantaneous line congruence},
url = {http://eudml.org/doc/250499},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Abdel-Baky, Rashad A.
AU - Al-Bokhary, Ashwaq J.
TI - A new approach for describing instantaneous line congruence
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 3
SP - 223
EP - 236
AB - 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.
LA - eng
KW - lines of curvature; line congruence; E. Study’s map; instantaneous revolution axis; lines of curvature; line congruence; E. Study's map; instantaneous revolution axis
UR - http://eudml.org/doc/250499
ER -

References

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