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

Authors : Ali ÇALIŞKAN

Pages : 0-0

Doi:10.1501/Commua1_0000000306

View : 17 | Download : 8

Publication Date : 1989-01-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(chosen as prîncipal ruled surfaces); R of a cong- mence R insert ignore into journalissuearticles values(u,v); are given in the section II so as to use in the third section. In the section three, the relation B = P insert ignore into journalissuearticles values( Cos 4? p B. + Sin İp d 4, “ds` + Ro); is found among the Blaschke vectors insert ignore into journalissuearticles values(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