# 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

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topAbdel-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 -

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