Reduction of Vaisman structures in complex and quaternionic geometry

Details Reduction of Vaisman structures in complex and quaternionic geometry Reduction of Vaisman structures in complex and quaternionic geometry

2005-02-28

arxiv.org/abs/math/0502572v2

J. Geom. Phys. 56 (2006), no. 12, 2501--2522

Mathematics

Differential Geometry

29 pages; Section 4 changed (and accordingly the Introduction); Remark 8.2 added; References updated

Scientific paper

10.1016/j.geomphys.2006.01.005

We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,\Gamma) where K is a Kaehler manifold and \Gamma a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kaehler manifold (K,\Gamma) as the rank of a natural quotient of \Gamma, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kaehler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover we define locally conformal hyperkaehler reduction as an equivariant version of hyperkaehler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally we show that locally conformal hyperkaehler reduction induces hyperkaehler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperkaehler reduction.

Affiliated with

Also associated with

No associations

Rating

Reduction of Vaisman structures in complex and quaternionic geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reduction of Vaisman structures in complex and quaternionic geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduction of Vaisman structures in complex and quaternionic geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-142560