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Special Kähler-Ricci potentials on compact Kähler manifolds | | A. Derdzinski
; G. Maschler
; | | Date: |
28 Apr 2002 | | Subject: | Differential Geometry MSC-class: Primary 53C55, 53C21 (Primary) 53C25 (Secondary) | math.DG | | Affiliation: | The Ohio State University), G. Maschler (University of Toronto | | Abstract: | A special Kähler-Ricci potential on a Kähler manifold is any nonconstant $C^infty$ function $ au$ such that $J(
abla au)$ is a Killing vector field and, at every point with $d au
e 0$, all nonzero tangent vectors orthogonal to $
abla au$ and $J(
abla au)$ are eigenvectors of both $
abla d au$ and the Ricci tensor. For instance, this is always the case if $ au$ is a nonconstant $C^infty$ function on a Kähler manifold $(M,g)$ of complex dimension $m>2$ and the metric $ ilde g=g/ au^2$, defined wherever $ au
e 0$, is Einstein. (When such $ au$ exists, $(M,g)$ may be called {it almost-everywhere conformally Einstein}.) We provide a complete classification of compact Kähler manifolds with special Kähler-Ricci potentials and use it to prove a structure theorem for compact Kähler manifolds of any complex dimension $m>2$ which are almost-everywhere conformally Einstein. | | Source: | arXiv, math.DG/0204328 | | Services: | Forum | Review | PDF | Favorites | |
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