The parameter rigid flows on oriented 3-manifolds

Shigenori Matsumoto

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arXiv · 1002.0188

The parameter rigid flows on oriented 3-manifolds

Shigenori Matsumoto

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Abstract

A flow defined by a nonsingular smooth vector field $X$ on a closed manifold $M$ is said to be parameter rigid if given any real valued smooth function $f$ on $M$, there are a smooth funcion $g$ and a constant $c$ such that $f=X(g)+c$ holds. We show that the parameter rigid flows on closed orientable 3-manifolds are smoothly conjugate to Kronecker flows on the 3-torus with badly approximable slope.

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Shigenori Matsumoto. 2010-02-01. The parameter rigid flows on oriented 3-manifolds. https://arxiv.org/abs/1002.0188

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