The Relation Among Blaschke Vectors Of Ruled Surfaces On A Line Congruence And Its Conseouences

Year 1989, Volume: 38 Issue: 01.02, - , 01.01.1989

Ali Çalışkan

https://doi.org/10.1501/Commua1_0000000306

Abstract

This study consists of three sections and first of them is reserved for the Basic con­ cepts. Necessary concepts and relations obtained among the magnıtudes of a ruled surface Rx and parameter ruled surfaces (chosen as prîncipal ruled surfaces) R of a cong- mence R (u,v) are given in the section II so as to use in the third section.
In the section three, the relation
B = P (
Cos 4? p
B. +
Sin İp d 4, “ds" + Ro)
is found among the Blaschke vectors (dual instantaneous speeds) of the three ruled surfaces mentioned in the seçtin II. Using this relation, the formula of Liouville, J. for the theory of surfaces is generalized to the line space by giving the relation among the dual splıerical cur- vaturs which are the invariants of the ruled surfaces, and some corollaries concernîng with thcme relations are given.

Keywords

Relation Among, Blaschke Vectors, Conseouences

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi