Characterizing Round Spheres Using Half-Geodesics

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 note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round

Existence and Non-existence of Half-Geodesics on S2S^2

In this paper we study half-geodesics, those closed geodesics that minimize on any subinterval of length $l(\gamma)/2$. For each nonnegative integer $n$, we construct Riemannian manifolds diffeomorphic to $S^2$ admitting exactly $n$ half-geodesics. Additionally, we construct a sequence of Riemannian manifolds, each of which is diffeomorphic to $S^2$ and admits no half-geodesics, yet which converge in the Gromov-Hausdorff sense to a limit space with infinitely many half-geodesics.Comment: This version has been shortened for publicatio

Garmin Aviation Software Engineering Internship

STEP Category: InternshipsSTEP presentation on summer software engineering internship at Garmin International.The Ohio State University Second-year Transformational Experience Program (STEP)Academic Major: Computer Science and Engineerin