Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.

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We have found an error in one of the results in our paper. Our claim in Eq. (3) is not true. According to the correct version, all the Weyl tensor components in de Sitter/anti-de Sitter spacetimes are zero identically and therefore give arbitrary WCs and not 10 as claimed in our paper.

This paper considers the symmetries of the curvature tensor (curvature collineations) and of the Weyl conformal tensor (Weyl conformal collineations) in general relativity. Some general results are reviewed for later application, some new ones proved and many special cases are investigated. Particular emphasis is laid on the interrelations between these two types of symmetries. A number of instructive examples of such symmetries are given.

Curvature collineations of some static spherically symmetric space–times are derived and compared with isometries and Ricci collineations for corresponding space–times.