Estimating the eigenvalues on Quaternionic Kähler Manifolds

英文摘要：

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.