I know that for compact (smooth) surfaces in $\mathbb R^3$ the 2-torus is the only surface that has vector fields with no zeroes. What happens if we take the compactness of the surface away? Does this still hold or can we find vector fields with zeros on surfaces other than the 2-torus then?
2026-04-30 10:16:33.1777544193
zeroes of vector fields on surfaces
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