Seifert conjecture

In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit.

In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture.

The existence of smoother counterexamples remained an open question until 1993 when Krystyna Kuperberg constructed a very different

Later this construction was shown to have real analytic and piecewise linear versions.

possess closed flowlines[1] based on similar results for Beltrami flows on the Weinstein conjecture.