*Wissenschaftliches Programm*   *Liste der Vortragenden*

Sektion 3
Montag, 18.09.2000, 14.00–14.50 Uhr, WIL A 120

Realization of special Kähler manifolds as parabolic hyperspheres

Vicente Cortés, Universität Bonn

The purpose of this talk is to relate some area of recent intense interest in mathematical physics, namely special Kähler manifolds, to the more classical subject of affine differential geometry. It is based on joint work with Oliver Baues (ETH Zürich). We prove that any simply connected special Kähler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic hypersphere to any nondegenerate holomorphic function. This generalizes a classical theorem of Blaschke about (2-dimensional) parabolic spheres to higher diomensions. Also, as an other application, we show that a classical result of Calabi and Pogorelov (1958/1972) on parabolic hyperspheres implies Lu’s theorem (1999) on complete special Kähler manifolds with a positive definite metric.