Applications of Riemannian Submersions

In this chapter, we give two applications of Riemannian submersions and it consists of two sections. In the first section, we give an application of Riemannian submersions in robotic theory [12]. To this aim, we first define Lie groups and give basic properties of such manifolds, then we give applications of Riemannian submersions in redundant robotic theory. Applications of Riemannian submersions in Kaluza-Klein theory have been given in detail in the book [111] and papers [112] and [40]; therefore, in the second section of this chapter, we give brief information for the Kaluza-Klein theory in terms of principal fiber bundles and Riemannian submersions.