A note on the Gauss maps of Cayley-free embeddings into spin(7)-manifolds. (English) Zbl 1398.53062
Summary: We show that a closed, orientable 4-manifold \(M\) admits a Cayley-free embedding into flat \(\mathrm{Spin}(7)\)-manifold \(\mathbb{R}^8\) if and only if both the Euler characteristic \(\chi_M\) and the signature \(\tau_M\) of \(M\) vanish.
MSC:
| 53C38 | Calibrations and calibrated geometries |
| 32U15 | General pluripotential theory |
| 32F17 | Other notions of convexity in relation to several complex variables |
| 57R40 | Embeddings in differential topology |
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