WebJul 22, 2015 · It is known that the shortest non-simple closed geodesic on an orientable hyperbolic 2-orbifold passes through an orbifold point of the orbifold (Nakanishi in Tohoku Math J (2) 41:527–541, 1989 ). This raises questions about minimal length non-simple closed geodesics disjoint from the orbifold points. WebSep 23, 2024 · We study the existence of closed geodesics on compact Riemannian orbifolds, and on noncompact Riemannian manifolds in the presence of a cocompact, isometric group action. We show that every noncontractible Riemannian manifold which admits such an action, and every odd-dimensional, compact Riemannian orbifold has a …

Introduction to Orbifolds - arXiv

Webof the S1-orbits of closed geodesics in a geometric equivalence class. In the last section, we sketch how the classical theory of closed geodesics on Riemannian man-ifolds can be adapted to the case of orbifolds. In sections 3, 4 and 5 we assume familiarity with the notions and the basic papers concerning the theory of closed Webbundle over a closed surface F.If F and the total space M are both ori-entable this bundle is determined by its Euler class e∈ Z.In general, the quotient space obtained by collapsing … screen printing tweed heads

Closed geodesic - Encyclopedia of Mathematics

Web2-orbifolds, e.g. for a sphere with three singular points of order 2, even the existence of a single closed geodesic in the regular part does not seem to be rigorously proven, yet. In WebIn particular, it makes sense to search for closed geodesics on Riemannian orbifolds [6,19, 12] and to investigate Besse orbifolds, that is, Riemannian orbifolds all of whose geodesics are closed ... WebExistence of closed geodesics on compact manifolds was first proved by Lyusternik and Fet in the 1950s using Morse theory, and the corresponding problem for orbifolds was studied by... screen printing tutorials pdf