Curvature collineations in certain gravitational space-times

It has been shown that the space-times formed from the product of two surfaces and from a thick gravitational plane wave sandwiched between two flat space-times admit proper curvature collineation in general. The curvature collineation vectors have been determined explicitly. For the space-time formed from the product of two surfaces conditions are obtained for it to admit motion. It has also been pointed out that the space-time formed from a thick plane gravitational wave belongs to the class (IIIsub(b)) of pure gravitational radiation and admits five- and six-parameter groups of motion in the two possible cases. Conservation laws given by Sachs and Katzin-Levine-Davis (J. Math. Phys.; 10:617 (1969)) in terms of curvature collineation vectors are satisfied identically in the case of the plane gravitational wave solution, and Sachs' conservation law can be deduced in this case as a consequence of the theorem given by Katzin and others. (author)