On Affine Normal Forms and a Classification of Homogeneous Surfaces in Affine Three-Space
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Blaschke, W.: Vorlesungen über Differentialgeometrie II, Springer-Verlag, 1923, Chelsea Co., 1967.
Doubrov, B., Komrakov, B. and Rabinovich, M.: Homogeneous surfaces in the three-dimensional affine geometry, in: F. Dillen et al. (eds), Geometry and Topology of Submanifolds, VIII, World Scientific, Singapore, 1996, pp. 168–178.
Gover, A. R.: The algebra of orthogonal group invariants, Preprint.
Guzeev, R. and Loboda, A.: On normal equations of affinely homogeneous convex surfaces of ℝ3-space (Russian), Preprint.
Hilbert, D. and Cohn-Vossen, S.: Geometry and the Imagination, Chelsea Publishing Co., New York, 1952.
Leichtweiß, K.: Über eine geometrische Deutung des Affinnormalenvektors einseitig gekrümmter Hyperflächen, Arch. Math. 53 (1989), 613–621.
Loboda, A.: On classification of affinely homogeneous surfaces in ℝ3-space in terms of their normal equations (Russian), Proceedings of ‘Pontryagin's Readings-6’, Voronezh-98, p. 124.
Loboda, A.: On determination of affinely homogeneous surfaces of ℝ3-space via the coefficients of its normal equations (Russian), Mat. Zametki, to appear.
Nomizu, K. and Sasaki, T.: A new model of unimodular-affinely homogeneous surfaces, Manuscripta Math. 73 (1991), 39–44.
Nomizu, K. and Sasaki, T.: On the classification of projectively homogeneous surfaces, Result. Math. 20 (1991), 698–724.
Nomizu, K. and Sasaki, T.: Affine Differential Geometry, Cambridge University Press, Cambridge, 1994.
Procesi, C.: The invariant theory of n × n matrices, Adv. Math. 19 (1976), 306–381.
Weyl, H.: The classical groups, their invariants and representations. Princeton University Press, Princeton, 1939.