On 4-dimensional almost paracomplex pure-Walker manifolds

In this thesis, firstly, an almost paracomplex manifolds with neutral metric was created and moved onto the Walker 4-manifolds with the help of transformation matrix. Secondly, for the almost paracomplex pure-Walker manifolds which is obtained on the Walker 4-manifolds, the conditions of integrability and some problems of the Kahler manifolds are investigated. Finally, an example is given to flat almost paracomplex pure-Walker manifolds which consists of a non-integrable almost paracomplex structures.