Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

研究成果: Article

5 引用 (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.

元の言語English
ページ（範囲）665-691
ページ数27
ジャーナルInternational Journal of Mathematics
巻17
発行部数6
DOI
出版物ステータスPublished - 2006 7
外部発表Yes

Fingerprint

Eigenvalue
Enveloping Algebra
First Eigenvalue
Differential operator
First-order
Symmetry
Operator
Estimate
Observation

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

Estimating the eigenvalues on quaternionic Kähler manifolds. / Homma, Yasushi.

：: International Journal of Mathematics, 巻 17, 番号 6, 07.2006, p. 665-691.

研究成果: Article

Homma, Y 2006, 'Estimating the eigenvalues on quaternionic Kähler manifolds', International Journal of Mathematics, 巻. 17, 番号 6, pp. 665-691. https://doi.org/10.1142/S0129167X06003643
Homma Y. Estimating the eigenvalues on quaternionic Kähler manifolds. International Journal of Mathematics. 2006 7;17(6):665-691. https://doi.org/10.1142/S0129167X06003643
Homma, Yasushi. / Estimating the eigenvalues on quaternionic Kähler manifolds. ：: International Journal of Mathematics. 2006 ; 巻 17, 番号 6. pp. 665-691.
@article{1b297d4ee03c4016b5cfc6758e8ddaca,
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",
year = "2006",
month = "7",
doi = "10.1142/S0129167X06003643",
language = "English",
volume = "17",
pages = "665--691",
journal = "International Journal of Mathematics",
issn = "0129-167X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "6",

}

TY - JOUR

T1 - Estimating the eigenvalues on quaternionic Kähler manifolds

AU - Homma, Yasushi

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

UR - http://www.scopus.com/inward/record.url?scp=33745916117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745916117&partnerID=8YFLogxK

U2 - 10.1142/S0129167X06003643

DO - 10.1142/S0129167X06003643

M3 - Article

AN - SCOPUS:33745916117

VL - 17

SP - 665

EP - 691

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 6

ER -

文献にアクセス