Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

doi:10.1142/S0129167X06003643

Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article

5 Citations (Scopus)

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 language	English
Pages (from-to)	665-691
Number of pages	27
Journal	International Journal of Mathematics
Volume	17
Issue number	6
DOIs	https://doi.org/10.1142/S0129167X06003643
Publication status	Published - 2006 Jul 1

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Keywords

Bochner-Weitzenböck formulas
Casimir elements
Quaternionic Kähler manifolds

ASJC Scopus subject areas

Mathematics(all)

Cite this

Homma, Y. (2006). Estimating the eigenvalues on quaternionic Kähler manifolds. International Journal of Mathematics, 17(6), 665-691. https://doi.org/10.1142/S0129167X06003643

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Access to Document

10.1142/S0129167X06003643