Estimating the eigenvalues on Quaternionic Kähler Manifolds

Details Estimating the eigenvalues on Quaternionic Kähler Manifolds Estimating the eigenvalues on Quaternionic Kähler Manifolds

2004-05-20

arxiv.org/abs/math/0405384v2

Mathematics

Differential Geometry

32page. minor revision including new observations

Scientific paper

We study geometric first order differential operators on quaternionic
K\"ahler 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-Weitzenb\"ock formulas for
operators. As an application, we estimate the first eigenvalues of them.

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