Ricci solitons and concurrent vector fields

This study is based on two chapters. In the first chapter, mainly used concepts of differential geometry is introduced with examples such that tensor fields, differential operators, tensor derivation, Ricci tensor, etc. Moreover, fundemental equations of the submanifold theory in Riemannian Geometry, which has a main role in differential geometry, and product manifolds are examined in this chapter. In the second chapter, "Ricci solitons and concurrent vector fields" has been studied and examined which was given by Bang-Yen Chen and Sharief Deshmukh in 2015. In particular, proofs of the theorems and propositions have been given with details about concurrent vector fields, warped product manifolds, submanifolds admitting Ricci solitons.