2006/10/17 by Wing Kai Ho, Ho, Wing Kai
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #53C20 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20
paper · pdf · doi:10.48550/arxiv.math/0610503
11 pages, 8 figures
arxiv created 2006/10/17 · openalex publication_date 2006/10/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is a question by C.Sormani that whether there exists a k ∈ \mathbb N, such that any compact, smooth and simply connected manifold has a 1/k-geodesic. We prove in this paper that this is not true by showing for each k, there exists a metric on the sphere such that it has no 1/k-geodesic.