Geodesic
Homogeneous Hypersurfaces with Isotropy in Affine Four-Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 57-70 
M. G. Eastwood; V. V. Ezhov. Homogeneous Hypersurfaces with Isotropy in Affine Four-Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 57-70. http://geodesic.mathdoc.fr/item/TM_2001_235_a3/
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     title = {Homogeneous {Hypersurfaces} with {Isotropy} in {Affine} {Four-Space}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

[1] Doubrov B., Komrakov B., Rabinovich M., “Homogeneous surfaces in the three-dimensional affine geometry”, Geometry and topology of submanifolds, VIII, eds. F. Dillen et al., World Sci., River Edge, NJ, 1996, 168–178 | MR | Zbl

[2] Eastwood M. G., Ezhov V. V., “On affine normal forms and a classification of homogeneous surfaces in affine three-space”, Geom. dedicata, 77 (1999), 11–69 | DOI | MR | Zbl

[3] Leichtweiß K., “Über eine geometrische Deutung des Affinnormalenvektors einseitig gekrümmter Hyperflächen”, Arch. Math., 53 (1989), 613–621 | DOI | MR | Zbl

[4] Loboda A. V., “Ob opredelenii affinno odnorodnoi sedlovidnoi poverkhnosti prostranstva $\mathbb{R}^3$ po koeffitsientam ee normalnogo uravneniya”, Mat. zametki, 65:5 (1999), 793–796 | MR

[5] Penrose R., Rindler W., Spinors and space–time, V. 1, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[6] Nomizu K., Sasaki T., Affine differential geometry, Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl