Symmetry structures and conservation laws of four-dimensional non-reductive homogeneous spaces

We investigate variational, Lie and Killing symmetries of the Lagrangian of an essential class of four- dimensional (pseudo-)Riemannian manifolds, i.e., non-reductive homogeneous spaces. Moreover, a Lie algebra analysis is shown. With the help of a result of the Noether's theorem, we have presented the expressions for conservation laws corresponding to all variational symmetries. (author)