Exceptional holonomy based on the Hitchin flow on complex line bundles

Details Exceptional holonomy based on the Hitchin flow on complex line bundles Exceptional holonomy based on the Hitchin flow on complex line bundles

2010-10-08

arxiv.org/abs/1010.1695v1

Mathematics

Differential Geometry

24 pages

Scientific paper

An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N_6 can be defined as a pair of a 2-form omega and a 3-form rho. Let M_8 be an arbitrary complex line bundle over N_6. We prove that any SU(3)- or SU(1,2)-structure on N_6 with d\omega^2=0 can be uniquely extended to a Spin(7)- or Spin_0(3,4)-structure which is defined on a tubular neighborhood of the zero section of M_8. As an application, we prove that the known cohomogeneity-one metrics with holonomy Spin(7) on a certain complex line bundle over SU(3)/U(1)^2 are the only ones.

Affiliated with

Also associated with

No associations

Rating

Exceptional holonomy based on the Hitchin flow on complex line bundles 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 Exceptional holonomy based on the Hitchin flow on complex line bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exceptional holonomy based on the Hitchin flow on complex line bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-486625