Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms

David M. J. Calderbank, Vladimir S. Matveev, Stefan Rosemann

Research output: Contribution to journalArticle

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Abstract

The mobility of a Kaehler metric is the dimension of the space of metrics with which it is c-projectively equivalent. The mobility is at least two if and only if the Kaehler metric admits a nontrivial hamiltonian 2-form. After summarizing this relationship, we present necessary conditions for a Kaehler metric to have mobility at least three: its curvature must have nontrivial nullity at every point. Using the local classification of Kaehler metrics with hamiltonian 2-forms, we describe explicitly the Kaehler metrics with mobility at least three and hence show that the nullity condition on the curvature is also sufficient, up to some degenerate exceptions. In an Appendix, we explain how the classification may be related, generically, to the holonomy of a complex cone metric.
Original languageEnglish
Pages (from-to)1555-1575
JournalCompositio Mathematica
Volume152
Issue number8
Early online date26 Apr 2016
DOIs
Publication statusPublished - 1 Aug 2017

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Curvature
Metric
Nullity
Holonomy
Form
Exception
Cone
Sufficient
If and only if
Necessary Conditions

Keywords

  • math.DG
  • 53B35, 53C55, 53B10, 53A20, 32J27, 53C25

Cite this

Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms. / Calderbank, David M. J.; Matveev, Vladimir S.; Rosemann, Stefan.

In: Compositio Mathematica, Vol. 152, No. 8, 01.08.2017, p. 1555-1575.

Research output: Contribution to journalArticle

Calderbank, David M. J. ; Matveev, Vladimir S. ; Rosemann, Stefan. / Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms. In: Compositio Mathematica. 2017 ; Vol. 152, No. 8. pp. 1555-1575.
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