Manifolds all of whose Geodesics are Closed [Hardcover]

0. Introduction.- A. Motivation and History.- B. Organization and Contents.- C. What is New in this Book?.- D. What are the Main Problems Today?.- 1. Basic Facts about the Geodesic Flow.- A. Summary.- B. Generalities on Vector Bundles.- C. The Cotangent Bundle.- D. The Double Tangent Bundle.- E. Riemannian Metrics.- F. Calculus of Variations.- G. The Geodesic Flow.- H. Connectors.- I. Covariant Derivatives.- J. Jacobi Fields.- K. Riemannian Geometry of the Tangent Bundle.- L. Formulas for the First and Second Variations of the Length of Curves.- M. Canonical Measures of Riemannian Manifolds.- 2. The Manifold of Geodesics.- A. Summary.- B. The Manifold of Geodesics.- C. The Manifold of Geodesics as a Symplectic Manifold.- D. The Manifold of Geodesics as a Riemannian Manifold.- 3. Compact Symmetric Spaces of Rank one From a Geometric Point of View.- A. Introduction.- B. The Projective Spaces as Base Spaces of the Hopf Fibrations.- C. The Projective Spaces as Symmetric Spaces.- D. The Hereditary Properties of Projective Spaces.- E. The Geodesics of Projective Spaces.- F. The Topology of Projective Spaces.- G. The Cayley Projective Plane.- 4. Some Examples of C- and P-Manifolds: Zoll and Tannery Surfaces.- A. Introduction.- B. Characterization of P-Metrics of Revolution on S2.- C. Tannery Surfaces and Zoll Surfaces Isometrically Embedded in (IR3, can).- D. Geodesics on Zoll Surfaces of Revolution.- E. Higher Dimensional Analogues of Zoll metrics on S2.- F. On Conformal Deformations of P-Manifolds: A. Weinsteins Result.- G. The Radon Transform on (S2, can).- H. V. Guillemins Proof of Funks Claim.- 5. Blaschke Manifolds and Blaschkes Conjecture.- A. Summary.- B. Metric Properties of a Riemannian Manifold.- C. The Allamigeon-Warner Theorem.- D. Pointed Blaschke Manifolds and Blaschke Manifolds.- E. Some Properties of Blaschke Manifolds.- F. Blaschkes Conjecture.- G. The K?hler Case.- H. An Infinitesimal Blaschke Conjecture.- 6. Harmonic Manifolds.- A. Introduction.- BlSC