Abstract
Motivated by the physical concept of special geometry, two mathematical constructions are studied which relate real hypersurfaces to tube domains and complex Lagrangian cones, respectively. Methods are developed for the calssification of homogeneous Riemannian hypersurfaces and the classification of linear transitive reductive algebraic group actions on pseudo-Riemannian hypersurfaces. The theory is applied to the case of cubic hypersurfaces, which is the one most relevant to special geometry, obtaining the solution of the two classification problems and the description of the corresponding homogeneous special Kähler manifolds.
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