Titlebook: Manifolds all of whose Geodesics are Closed; Arthur L. Besse Book 1978 Springer-Verlag Berlin Heidelberg 1978 Geodätische Linie.Manifolds.

法律的瑕疵

闲聊

Harmonic Manifolds,Let . be a ROSS (see 3.16). The fact that its isometry group is transitive on . or on pairs of equidistant points implies that a lot of things do not really depend on . and . in . but only on the distance between them ϱ(.). We shall mainly consider two objects.

venous-leak

Foliations by Geodesic Circles,A.1. Let . be a .-manifold with a .-foliation by circles. We prove the following theorem of A.W. Wadsley [WY 2]:

显而易见

offense

,Blaschke Manifolds and Blaschke’s Conjecture,tance function and the notion of a segment; recall that segments are necessarily geodesies and locally unique. We define the cut-value and the cut-point of a geodesic. We recall the strict triangle inequality and the acute angle property. Finally we define what a manifold with spherical cut-locus is.

臆断

On the Topology of SC- and P-Manifolds,s of .-manifolds which are not isometric to a CROSS, the so-called Zoll manifolds. Observe, however, that the underlying differentiable manifold in these examples is the standard sphere. In this chapter we will prove that, at least topologically, the .-manifolds are not very different from CROSSes. The main result we prove is the following.

GREG

https://doi.org/10.1007/978-3-642-61876-5Geodätische Linie; Manifolds; Riemannian geometry; Riemannian manifold; Riemannsche Mannigfaltigkeit; cur

准则

清晰

Basic Facts about the Geodesic Flow,It only assumes a basic knowledge of differential geometry such as manifolds, differentiable maps, the tangent functor, exterior differential forms and the exterior differential, vector fields and the Lie derivative. Good references for this material are [AM], [GO 1], [SG], [WR 3]..It does not conta

Fsh238

The Manifold of Geodesics,the manifold of geodesies . for a .-manifold and we relate its tangent spaces to normal Jacobi fields. The existence of a nondegenerate closed two-form on .. is the most striking fact. This form endows the manifold with a symplectic structure. Using the fact that the unit tangent bundle of . is fibe