Almost paracontact almost paracomplex Riemanian manifolds

In this thesis, almost paracontact almost paracomplex Riemannian manifolds and para Sasaki like manifolds which is a special class of these manifolds are discussed. For the classification of these manifolds, the fundamental tensor field of type (0,3) is used and these manifolds are divided into 11 basic classes. Almost paracontact almost paracomplex Riemann metric structure on three dimensional Lie algebras was examined and classified. From this point of view, this structure is examined on five dimensional nilpotent Lie algebras and it is investigated whether there are para Sasaki like, para Einstein like and para Ricci like solitons. Generalized symmetric metric connection on almost paracontact almost paracomplex Riemannian metric manifolds is discussed. Generalized symmetric metric connection on three dimensional Lie algebras and five dimensional nilpotent Lie algebras is considered.