Geodesic
Homogeneous Hypersurfaces with Isotropy in Affine Four-Space
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 57-70

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We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional. 
@article{TRSPY_2001_235_a3,
     author = {M. G. Eastwood and V. V. Ezhov},
     title = {Homogeneous {Hypersurfaces} with {Isotropy} in {Affine} {Four-Space}},
     journal = {Informatics and Automation},
     pages = {57--70},
     publisher = {mathdoc},
     volume = {235},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2001_235_a3/}
}
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M. G. Eastwood; V. V. Ezhov. Homogeneous Hypersurfaces with Isotropy in Affine Four-Space. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 57-70. http://geodesic.mathdoc.fr/item/TRSPY_2001_235_a3/