 | |
Papers - Locally conformal Kaehler reduction | |
|
 | |
|
Locally conformal Kähler reduction
Abstract
We define reduction of locally
conformal Kähler manifolds, considered as conformal Hermitian
manifolds, and we show its equivalence with an unpublished
construction given by Biquard and
Gauduchon.
We show the compatibility between this reduction and
Kähler reduction of the universal cover. By a recent result of
Kamishima and
Ornea, in the Vaisman case
(that is, when a metric in the conformal class has parallel Lee
form) if the manifold is compact
its universal cover comes equipped with the
structure of Kähler cone over a Sasaki compact manifold.
We show the compatibility between our reduction and Sasaki
reduction, hence describing
a subgroup of automorphisms whose action causes reduction to bear a Vaisman structure.
Then we apply
this theory
to construct a wide class of Vaisman manifolds.
|
|
|
| |
|
|
|
|
