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On the director surface of a rectilinear congruence

Published online by Cambridge University Press:  24 October 2008

P. Jha  and
C. J. Eliezer
P. Jha
Affiliation:
University of Malaya, Kuala Lumpur
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Extract

In this paper, it is shown that certain quantities defined with reference to the rays of a rectilinear congruence, remain unchanged for a change in the director surface, provided that the spherical representation of the congruence is kept unchanged. These quantities may be called semi-invariants. Some known invariants have been expressed in terms of these semi-invariants. An attempt has been made to find how these semi-invariants alter when the parametric curves are changed in any manner.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 503 - 504
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCE

(1)Weatherburn, C. E., Differential geometry, vol. I (Cambridge, 1927).Google Scholar