The geometry of biwarped product submanifolds

The aim of this thesis is to examine a certain type of biwarped product submanifolds of locally product Riemannian manifolds. This thesis consists of six sections. In the first chapter, the subject of the thesis is presented. The second part is divided into three subsections. In the first subsection, the concepts of Riemannian manifold and submanifold are mentioned. In the second subsection, multiply warped product manifolds, which we will focus on this thesis, are mentioned. In the third subsection, we recall that the well known some submanifolds of locally product Riemannian manifolds such as invariant, anti-invariant, slant, semi-invariant, semi-slant and hemi-slant. In the third chapter, tools and methods that are used through the thesis are mentioned. The fourth chapter the main part of our thesis. In this section, we consider and study of the biwarped product submanifold of locally product Riemannian manifold whose base factor is proper slant and the one of the fiber factor is invariant and the other fiber factor is anti-invariant. First of all, the existence theorem has been proved for such submanifolds. Later, the necessary and sufficient conditions for such submanifolds to be warped products are given. In addition, a general inequality for such submanifolds has been constructed and the equality case of this inequality has been examined. Finally, an application of this inequality is given. In the fifth chapter, a general evaluation of this thesis study is made. In the last chapter, the studies used in this thesis are listed.