We investigate the form of Killing tensors, constructed from conformal Killing vectors of a given spacetime (M, g), by utilizing the Koutras algorithm. As an example we find irreducible Killing tensors in Robertson-Walker spacetimes. A number of theorems axe given for the existence of Killing tensors in the conformally related spacetime (M, g). The form of the conformally related Killing tensors are explicitly determined. The conditions on the conformal factor Omega relating the two spacetimes (M, g) and (M, g) are determined for the existence of the tensors. Also we briefly consider the role of recurrent vectors, inheriting conformal vectors and gradient conformal vectors in building Killing tensors. [References: 22]
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