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EXTREMAL KAHLER METRICS ON RULED MANIFOLDS AND STABILITY
 

Summary: EXTREMAL K¨AHLER METRICS ON RULED
MANIFOLDS AND STABILITY
by
Vestislav Apostolov, David M. J. Calderbank, Paul Gauduchon
& Christina W. Tønnesen-Friedman
Abstract. -- This article gives a detailed account and a new presentation of
a part of our recent work [3] in the case of admissible ruled manifolds without
blow-downs. It also provides additional results and pieces of information that
have been omitted or only sketched in [3].
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1. Extremal metrics on admissible ruled manifolds . . . . . . . . . . 4
1.1. Admissible ruled manifolds . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2. Admissible K¨ahler classes . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3. Admissible momenta and K¨ahler metrics . . . . . . . . . . 7
1.4. Admissible momentum profiles . . . . . . . . . . . . . . . . . . . . 8
1.5. Standard admissible metrics . . . . . . . . . . . . . . . . . . . . . . 9
1.6. Symmetries of admissible K¨ahler metrics . . . . . . . . . . 10
1.7. Ricci form and scalar curvature . . . . . . . . . . . . . . . . . . 13
1.8. Hamiltonian 2-forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

  

Source: Apostolov, Vestislav - Département de mathématiques, Université du Québec à Montréal

 

Collections: Mathematics