Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

doi:10.1142/S0129167X06003643

Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

Research output: Contribution to journal › Article › peer-review

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
Externally published	Yes

Keywords

Bochner-Weitzenböck formulas
Casimir elements
Quaternionic Kähler manifolds

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X06003643

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title = "Estimating the eigenvalues on quaternionic K{\"a}hler manifolds",

abstract = "We study geometric first order differential operators on quaternionic K{\"a}hler 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{\"o}ck formulas for operators. As an application, we estimate their first eigenvalues.",

keywords = "Bochner-Weitzenb{\"o}ck formulas, Casimir elements, Quaternionic K{\"a}hler manifolds",

author = "Yasushi Homma",

note = "Funding Information: The author was partially supported by the Grant-in-Aid for JSPS Research Fellowships for Young Scientists.",

year = "2006",

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AU - Homma, Yasushi

N1 - Funding Information: The author was partially supported by the Grant-in-Aid for JSPS Research Fellowships for Young Scientists.

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - Bochner-Weitzenböck formulas

KW - Casimir elements

KW - Quaternionic Kähler manifolds

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