# THE MANHEIM AND LIOVILLE FORMULAE BY THE BLASCHKE VECTORS IN R31

• Ozyilmaz, Emin (Department of Mathematics, Faculty of Science, University of Ege)
• Received : 2014.08.12
• Accepted : 2014.09.15
• Published : 2014.12.25
• 124 22

#### Abstract

In this study, it is aimed to analyze how relationship among Blaschke vectors that the obtained formulae in [2, 3] change if parameter ruled surfaces of the spacelike line congruence are not choosed as principle ruled surfaces. Moreover, using the relation among Blaschke vectors, we obtain Manheim's and Liouville's formulae. This new method can be applied to congruences. Thus, we can obtain new formulae in lines space.

#### Keywords

dual space;Blaschke trihedron;dual curvature

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