Biconservative hypersurfaces in semi-euclidean spaces

In this study, prepared as a master's thesis, the geometric properties of biconservative hypersurfaces in Euclidean and semi-Euclidean spaces were investigated based on references [1–4]. This master's thesis was prepared in four chapters. The first chapter is the introduction section and information is given about the development of biconservative surfaces and hypersurfaces and their place in the literature. The second chapter is devoted to the basic concepts necessary for a better understanding of the subject. In this chapter, concepts related to semi-Riemannian manifolds, differential operators defined on these manifolds, submanifolds and basic properties of submanifolds are given. In the third chapter, firstly, biconservative hypersurfaces in 3 and 4 dimensional Euclidean spaces are investigated and the related characterization theorems are given in the first subsection. In the second subsection of the third chapter, biconservative hypersurfaces with three distinct principal curvatures in an arbitrary dimensional Euclidean space are studied and theorems and results are given about them. The fourth chapter, which is the last section of the thesis, consists of two subsections. Here, first, a classification of biconservative surfaces in Minkowski 3-space is given. Second, a classification is made for biconservative surfaces of the space forms of the semi-Euclidean spaces R^4_1 and R^4_2.