Vanshing Theorems for Quaternionic Kaehler Manifolds

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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.
26 Pages, LaTeX2e

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Differential Geometry, 53C25 (Primary) 58J50 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/58519

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0001061
 http://arxiv.org/abs/math/0001061

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arXiv