Noether symmetries of some space-times

In the first chapter of this study, an introduction in which aim of the thesis is explained has been begun and in the second chapter, the fundamental definitions have been given. In the third chapter, generalized gravity theories and Noether symmetry concepts to be used as a material and method have been explained.In this thesis, it has been obtained some exact cosmological solutions in gravity theory which is generalization of the Einstein-Hilbert Lagrangian. Firstly, the solutions have been investigated for the Local rotational symmetric Bianchi I, III and Kantowski-Sachs space time in the scalar tensor theories. Later, Noether symmetries of other Bianchi type space-times in scalar tensor theories have been studied. Metric potentials for Bianchi I space-times have also been obtained in the framework of f (R) gravity theory which is the other important generalized gravitation theory. In both gravitation theories, the Lagrange functional invariant under a Lie transformation is taken into account the Noether symmetry approach. The existence of Noether symmetry allows us to choose the coupling function and the potential of scalar field in the first theory and the form of f(R) function in the second theory. Moreover, such a symmetry also permits to find some transformations which simplify the field equations. Solutions of the field equations for taken into account the space-times have been investigated by using these transformations.