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RECENT PROGRESS ON CLOSED GEODESICS IN SOME COMPACT SIMPLY CONNECTED MANIFOLDS
Preview AbstractIn recent years, new interests on the problem of closed geodesics on spheres as well as compact simply connected manifolds increase and many new works have appeared. In this article, I give a brief survey on this problem, and describe the main ideas of the new results of H. Duan and myself on the existence of at least two distinct closed geodesics on every 3 or 4 dimensional compact simply connected manifold with an irreversible or reversible Finsler as well as Riemannian metric.