Twistor Geometry of Null Foliations in Complex Euclidean Space
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.3842/SIGMA.2017.005 |
| Field | General mathematics |
| Keywords | twistor geometry; complex variables; foliations; spinors |
| Description | We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear subspaces of maximal dimension of $\mathcal{Q}^n$. Viewing complex Euclidean space $\mathbb{CE}^n$ as a dense open subset of $\mathval{Q}^n$ , we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on $\mathbb{CE}^n$ can be constructed in terms of complex submanifolds of $\mathbb{PT}$. The construction is illustrated by means of two examples, one involving conformal Killing spinors, the other, conformal Killing– Yano 2-forms. We focus on the odd-dimensional case, and we treat the even-dimensional case only tangentially for comparison. |
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