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The non-existence of non-trivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.1991 Mathematics Subject Classification. 53C50, 53B30.

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Left-invariant Cotton solitons on homogeneous manifolds are determined. Moreover, algebraic Cotton solitons are studied providing examples of non-invariant Cotton solitons, both in the Riemannian and Lorentzian homogeneous settings.1991 Mathematics Subject Classification. 53C50, 53B30.

a b s t r a c tWe determine all left-invariant Ricci collineations on three-dimensional Lie groups.