Inequalities on manifolds

This study, which is prepared as a master thesis, consists of four chapters. In the rst chapter, some information is given about inequlities of manifolds. Also, in this section, the historical development of inequalities on manifolds to be considered in the thesis was mentioned. The second part is devoted to the basic concepts of differentiable manifolds, Riemann manifolds, submanifolds, the curvatures and Hermitian manifolds. In the third chapter, inequalities are established by using Ricci curvatures of Riemannian manifolds and Riemann submanifolds and geometrical results are given about these inequalities. In the fourth part of the thesis, inequalities on submanifolds of complex space forms and generalized complex space forms were examined. In addition, inequalities on Riemanian and Kaehler product manifolds were examined.