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arXiv · 1702.01282

Elliptic complex on the Grassmannian of oriented 2-planes

Tomas Salac
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Abstract

The Grassmannian $V_2(\mathbb{R}^{n+2})$ of oriented 2-planes in $\mathbb R^{n+2}$ where $n\ge3$ carries a homogeneous parabolic contact structure of Grassmannian type. The main result of this article is that on $V_2(\mathbb{R}^{n+2})$ lives an elliptic complex of invariant differential operators of length 3 which starts with the 2-Dirac operator and that the index of the complex is zero.

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Tomas Salac. 2018-02-16. Elliptic complex on the Grassmannian of oriented 2-planes. https://doi.org/10.1007/s00006-018-0817-3

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