Tight Beltrami fields with symmetry

Details Tight Beltrami fields with symmetry Tight Beltrami fields with symmetry

2006-12-13

arxiv.org/abs/math/0612334v2

Geom. Dedicata 134 (2008), 217--238

Mathematics

Differential Geometry

26 pages

Scientific paper

10.1007/s10711-008-9258-9

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 $\xi=\ker\alpha$.

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