Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Central Kähler metrics with non-constant central curvature

Authors: Andrew D. Hwang and Gideon Maschler
Journal: Trans. Amer. Math. Soc. 355 (2003), 2183-2203
MSC (2000): Primary 53C55, 53C25
Published electronically: January 31, 2003
MathSciNet review: 1973987
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C55, 53C25

Retrieve articles in all journals with MSC (2000): 53C55, 53C25

Additional Information

Andrew D. Hwang
Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610

Gideon Maschler
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

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)
Article copyright: © Copyright 2003 American Mathematical Society