Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

doi:10.1142/S0129167X06003643

Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma^*

^*この研究の対応する著者

研究成果: Article › 査読

5 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	665-691
ページ数	27
ジャーナル	International Journal of Mathematics
巻	17
号	6
DOI	https://doi.org/10.1142/S0129167X06003643
出版ステータス	Published - 2006 7月
外部発表	はい

ASJC Scopus subject areas

数学 (全般)

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10.1142/S0129167X06003643

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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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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.

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KW - Casimir elements

KW - Quaternionic Kähler manifolds

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Estimating the eigenvalues on quaternionic Kähler manifolds

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