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Estimating the eigenvalues on Quaternionic K\"ahler Manifolds

Differential Geometry 2007-05-23 v2

Abstract

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)\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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Cite

@article{arxiv.math/0405384,
  title  = {Estimating the eigenvalues on Quaternionic K\"ahler Manifolds},
  author = {Yasushi Homma},
  journal= {arXiv preprint arXiv:math/0405384},
  year   = {2007}
}

Comments

32page. minor revision including new observations