Characterizing round spheres using half-geodesics.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 31262829.
- Also identified by DOI 10.1073/pnas.1907226116 and PMC identifier 6642414.
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Abstract
A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this paper establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.