Geodesic
Cayley Hypersurfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 241-244

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We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, that generalize the Cayley surface. 
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     author = {M. G. Eastwood and V. Ezhov},
     title = {Cayley {Hypersurfaces}},
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M. G. Eastwood; V. Ezhov. Cayley Hypersurfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 241-244. http://geodesic.mathdoc.fr/item/TM_2006_253_a17/