Estimating the eigenvalues on Quaternionic Kähler Manifolds

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We study geometric first order differential operators on quaternionic Kähler manifolds. Their principal symbols are related to the enveloping algebra and Casimir elements for $\Sp(1)\Sp(n)$. This observation leads to anti-symmetry of the principal symbols and Bochner-Weitzenböck formulas for operators. As an application, we estimate the first eigenvalues of them.
32page. minor revision including new observations

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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/95096

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405384
 http://arxiv.org/abs/math/0405384

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arXiv