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arXiv · 1110.3279

Reduction of beta-integrable 2-Segre structures

Thomas Mettler
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Abstract

We show that locally every beta-integrable (2,n)-Segre structure can be reduced to a torsion-free S^1*GL(n,R)-structure. This is done by observing that such reductions correspond to sections with holomorphic image of a certain `twistor bundle'. For the homogeneous (2,n)-Segre structure on the oriented 2-plane Grassmannian, the reductions are shown to be in one-to-one correspondence with the smooth quadrics in CP^{n+1} without real points.

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Thomas Mettler. 2013-03-22. Reduction of beta-integrable 2-Segre structures. https://doi.org/10.4310/cag.2013.v21.n2.a3

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