Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action

Details Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action

1998-08-31

arxiv.org/abs/math/9808134v2

Mathematics

Differential Geometry

18 pages, AMS-Latex, replaced with a final version (minor corrections) on 14.01.1999; to appear in Math. Ann

Scientific paper

We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkaehler quotient of a flat quaternionic vector space by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n-1 whose isometry group has rank n+1 is isometric to a 3-Sasakian quotient of a sphere by a torus. As a corollary, a compact connected quaternion-Kaehler 4n-manifold with positive scalar curvature and isometry group of rank n+1 is isometric to the quaternionic projective space or the complex grassmanian.

Affiliated with

Also associated with

No associations

Rating

Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action 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 Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-503293