Estimating the eigenvalues on quaternionic Kähler manifolds

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Abstract

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 their first eigenvalues.

Original languageEnglish
Pages (from-to)665-691
Number of pages27
JournalInternational Journal of Mathematics
Volume17
Issue number6
DOIs
Publication statusPublished - 2006 Jul 1

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Keywords

  • Bochner-Weitzenböck formulas
  • Casimir elements
  • Quaternionic Kähler manifolds

ASJC Scopus subject areas

  • Mathematics(all)

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