### Abstract

Original language | English |
---|---|

Pages (from-to) | 1555-1575 |

Journal | Compositio Mathematica |

Volume | 152 |

Issue number | 8 |

Early online date | 26 Apr 2016 |

DOIs | |

Publication status | Published - 1 Aug 2017 |

### Fingerprint

### Keywords

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

### Cite this

*Compositio Mathematica*,

*152*(8), 1555-1575. https://doi.org/10.1112/S0010437X16007302

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

Research output: Contribution to journal › Article

*Compositio Mathematica*, vol. 152, no. 8, pp. 1555-1575. https://doi.org/10.1112/S0010437X16007302

}

TY - JOUR

T1 - Curvature and the c-projective mobility of Kaehler metrics with hamiltonian 2-forms

AU - Calderbank, David M. J.

AU - Matveev, Vladimir S.

AU - Rosemann, Stefan

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

KW - math.DG

KW - 53B35, 53C55, 53B10, 53A20, 32J27, 53C25

UR - http://dx.doi.org/10.1112/S0010437X16007302

U2 - 10.1112/S0010437X16007302

DO - 10.1112/S0010437X16007302

M3 - Article

VL - 152

SP - 1555

EP - 1575

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

IS - 8

ER -