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math.DG2022
The conjugate locus in convex 3-manifolds
Thomas Waters, Matthew Cherrie
In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent…
math.DG2022
The normal map as a vector field
Thomas Waters, Matthew Cherrie
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincaré index, i…
math.DG2017
Integrable geodesic flows on tubular sub-manifolds
Thomas Waters
In this paper we construct a new class of surfaces whose geodesic flow is integrable (in the sense of Liouville). We do so by generalizing the notion of tubes about curves to 3-dim…