Abstract
\noindent In this note, we prove that the shortest curve joining two points on a sphere in a real Hilbert space of dimension greater than $2$, lies in the great circle through these points. Our arguments will apply to all continuous curves on the sphere, not just to those that have tangent and principal normal vectors and curvature at each point.
Citation
F. S. Cater. "On the Curves of Minimal Length on Spheres in Real Hilbert Spaces." Real Anal. Exchange 25 (2) 781 - 786, 1999/2000.
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