Almost contact B-metric manifolds

In this thesis, the classification of almost contact B−metric manifolds are examined. Firstly, some basic definitions and theorems regarding almost contact manifolds, almost contact B−metric manifolds, and Sasaki-like almost contact B−metric manifolds are given. It is shown that D−homothetic deformation of Sasaki-like almost contact B−metric manifolds is also Sasaki-like almost contact B−metric manifold. It is proved that the product of two almost contact B−metric manifolds with given a complex structure and a B−metric is a almost complex B−metric manifold. The classification of almost contact B−metric manifolds is done and some examples of these are investigated. It is determined which class of Sasaki-like almost contact B−metric manifolds fall into. D−homothetic deformation of almost contact B−metric manifolds within certain class is shown to be within the same class. In the last part of the thesis which is original, the contact B−metric structures are studied on 5−dimensional nilpotent Lie algebras. It is investigated which class of 5-dimensional nilpotent Lie algebras with the B−metric structure fall into.