# Ramadanov conjecture and line bundles over compact Hermitian symmetric spaces Artikel i vetenskaplig tidskrift, 2010

We compute the Szegö kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in \mathbb CnCn for Grassmannian manifolds of higher ranks. In particular, they provide an infinite family of smoothly bounded strictly pseudoconvex domains on complex manifolds for which the logarithmic term in the Fefferman expansion of the Szegö kernel vanishes but whose boundary is not diffeomorphic to the sphere (in fact, it is not even locally spherical). The analogous results for the Bergman kernel are also obtained.

## Författare

#### M. Englis

Slezska univerzita v Opave

#### Genkai Zhang

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

#### Mathematische Zeitschrift

0025-5874 (ISSN) 1432-8232 (eISSN)

Vol. 264 901-912

Matematik

#### DOI

10.1007/s00209-009-0495-x