## Tight Beltrami fields with symmetry

### Abstract

Let $M$ be a compact orientable Seifered fibered 3-manifold without a boundary, and $\alpha$ an $S^1$-invariant contact form on $M$. In a suitable adapted Riemannian metric to $\alpha$, we provide a bound for the volume $\text{Vol}(M)$ and the curvature, which implies the universal tightness of the contact structure $\xi=\ker\alpha$.Comment: 26 page

Topics: Mathematics - Differential Geometry, Mathematics - Symplectic Geometry
Publisher: 'Springer Science and Business Media LLC'
Year: 2008
DOI identifier: 10.1007/s10711-008-9258-9
OAI identifier: oai:arXiv.org:math/0612334

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