Geodesic
Affine Homogeneity of Indefinite Real Hypersurfaces in the Space~$\mathbb{C}^3$
Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 867-884

Voir la notice de l'article provenant de la source Math-Net.Ru

We develop a constructive approach to the problem of describing affinely homogeneous real hypersurfaces in $3$-dimensional complex space having nondegenerate sign-indefinite Levi form. We construct the affine invariants of a nondegenerate indefinite hypersurface in terms of second-order jets of its defining function and introduce the notion of the affine canonical equation of this surface. Three main types of canonical equations are considered. For each of these types, we construct a family of Lie algebras related to affinely homogeneous surfaces of a particular type. As a result, a family (depending on two real parameters) of affinely different homogeneous submanifolds of $3$-dimensional complex space is presented (as matrix algebras).
Keywords: affinely homogeneous indefinite hypersurface, complex space $\mathbb{C}^3$, Lie algebra, strictly pseudoconvex hypersurface, Levi form, Hermitian form, canonical equation of an indefinite surface. 
@article{MZM_2010_88_6_a6,
     author = {M. S. Danilov and A. V. Loboda},
     title = {Affine {Homogeneity} of {Indefinite} {Real} {Hypersurfaces} in the {Space~}$\mathbb{C}^3$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {867--884},
     publisher = {mathdoc},
     volume = {88},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a6/}
}
TY  - JOUR
AU  - M. S. Danilov
AU  - A. V. Loboda
TI  - Affine Homogeneity of Indefinite Real Hypersurfaces in the Space~$\mathbb{C}^3$
JO  - Matematičeskie zametki
PY  - 2010
SP  - 867
EP  - 884
VL  - 88
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a6/
LA  - ru
ID  - MZM_2010_88_6_a6
ER  - 
%0 Journal Article
%A M. S. Danilov
%A A. V. Loboda
%T Affine Homogeneity of Indefinite Real Hypersurfaces in the Space~$\mathbb{C}^3$
%J Matematičeskie zametki
%D 2010
%P 867-884
%V 88
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a6/
%G ru
%F MZM_2010_88_6_a6
M. S. Danilov; A. V. Loboda. Affine Homogeneity of Indefinite Real Hypersurfaces in the Space~$\mathbb{C}^3$. Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 867-884. http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a6/