## Central Kähler metrics with non-constant central curvature

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- by Andrew D. Hwang and Gideon Maschler
- Trans. Amer. Math. Soc.
**355**(2003), 2183-2203 - DOI: https://doi.org/10.1090/S0002-9947-03-03158-1
- Published electronically: January 31, 2003
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## Abstract:

The*central curvature*of a Riemannian metric is the determinant of its Ricci endomorphism, while the scalar curvature is its trace. A Kähler metric is called

*central*if the gradient of its central curvature is a holomorphic vector field. Such metrics may be viewed as analogs of the extremal Kähler metrics defined by Calabi. In this work, central metrics of non-constant central curvature are constructed on various ruled surfaces, most notably the first Hirzebruch surface. This is achieved via the momentum construction of Hwang and Singer, a variant of an ansatz employed by Calabi (1979) and by Koiso and Sakane (1986). Non-existence, real-analyticity and positivity properties of central metrics arising in this ansatz are also established.

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## Bibliographic Information

**Andrew D. Hwang**- Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
- Email: ahwang@mathcs.holycross.edu
**Gideon Maschler**- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
- Email: maschler@math.toronto.edu
- Received by editor(s): November 1, 1999
- Published electronically: January 31, 2003
- Additional Notes: The first author was supported in part by an NSERC Canada individual research grant.

The second author was partially supported by the Edmund Landau Center for research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany) - © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**355**(2003), 2183-2203 - MSC (2000): Primary 53C55, 53C25
- DOI: https://doi.org/10.1090/S0002-9947-03-03158-1
- MathSciNet review: 1973987