On the decomposition theorems

This thesis covers four chapters such a way the first chapter is devoted to the introduction. In the second chapter , we give basic definitions and theorems which will be used in the other chapters.In the third chapter, after we investigate warped product manifolds,their geodesics and curvatures, we present twisted product manifolds. We also give decomposition theorems for such manifolds.In the fourth chapter, we introduce the notion of oblique warped products and give examples. Then we define convolution of Riemannian manifolds, give examples and investigate necessary and sufficient conditions for a factor of a convolution Riemannian manifold to be totally geodesic. We also obtain convolution of Euclidean submanifolds.