Closed Geodesics in Compact Riemannian Good Orbifolds and Horizontal Periodic Geodesics of Riemannian Foliations

In this paper we prove the existence of closed geodesics in certain types of compact Riemannian good orbifolds. This gives us an elementary alternative proof of a result due to Guruprasad and Haefliger. In addition, we prove some results about horizontal periodic geodesics of Riemannian foliations and stress the relation between them and closed geodesics in Riemannian orbifolds. In particular we note that each singular Riemannian foliation with flat sections and compact leaves on a compact simply connected space has horizontal periodic geodesics in each section.