Cotton solitons on 3-dimensional almost 𝜶-paracosymplectic manifolds

The primary goal of this thesis is to study Cotton solitons in almost 𝛼-paracosymplectic manifolds that are three-dimensional. The first section consists of the introduction. The second section includes three subsections. In section 2.1, basic definitions and theorems about vector spaces, linear transformations and tensors are presented. In Section 2.2, symmetric bilinear forms and the concept of index are emphasised in general. In Section 2.3, definitions and theorems that will be used frequently in the following chapters are presented. Semi-Riemannian manifolds, Semi-Riemannian connection, Riemannian curvature tensor, Ricci curvature tensor, Einstein manifold and scalar curvature are some of the basic concepts mentioned. The third section consists of six subsections. In Section 3.1, almost paracontact manifold and its properties are presented. In Section 3.2, the definition of almost paracomplex manifold and the concept of normality of almost paracomplex structure are presented. In Section 3.3, the metric tensor field is added to the manifolds mentioned in Section 3.1 and thus the properties of almost paracontact metric manifolds are given. Section 3.4 and Section 3.5 are devoted to the definition and properties of 𝐾-paracontact manifolds and Para-Sasakian manifolds respectively. Section 3.6 gives the definition and properties of almost 𝛼-paracosymplectic manifolds used in the original results of the thesis. The fourth section consists of original results. In 2021, Chen studied Cotton solitons in three-dimensional metric manifolds. In this thesis, Cotton solitons were studied on almost 𝛼-paracosymplectic metric manifolds which investigated by Küpeli Erken, Dacko and Murathan in 2015. The fifth section consists of conclusions and recommendations.