Vanshing Theorems for Quaternionic Kaehler Manifolds

Details Vanshing Theorems for Quaternionic Kaehler Manifolds Vanshing Theorems for Quaternionic Kaehler Manifolds

2000-01-11

arxiv.org/abs/math/0001061v1

Mathematics

Differential Geometry

26 Pages, LaTeX2e

Scientific paper

We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For quaternionic Kaehler manifolds this leads to simple proofs of eigenvalue estimates for Dirac and Laplace operators. Moreover it enables us to determine which representations can contribute to harmonic forms. As a corollary we prove the vanishing of certain odd Betti numbers on compact quaternionic Kaehler manifolds of negative scalar curvature. We simplify the proofs of several related results in the positive case.

Affiliated with

Also associated with

No associations

Rating

Vanshing Theorems for Quaternionic Kaehler Manifolds 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 Vanshing Theorems for Quaternionic Kaehler Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanshing Theorems for Quaternionic Kaehler Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-364927