We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions ...

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the ...

The present thesis is devoted to the study of closed geodesics in some types of orbifolds. First, we present the notion of Riemannian foliation and their equivalent definitions using foliation atlas and Riemannian submersions. ...

For a given Hilbert space H, consider the space of self-adjoint projections P(H). In this paper we study the differentiable structure of a canonical sphere bundle over P(H) given by R={(P,f)∈P(H)×H:Pf=f,‖f‖=1}.We establish ...