Estimating the eigenvalues on quaternionic Kähler manifolds

Yasushi Homma

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

Fingerprint

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

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: International Journal of Mathematics, Vol. 17, No. 6, 07.2006, p. 665-691.

Research output: Contribution to journal › Article

Homma, Y 2006, 'Estimating the eigenvalues on quaternionic Kähler manifolds', International Journal of Mathematics, vol. 17, no. 6, pp. 665-691. https://doi.org/10.1142/S0129167X06003643
Homma Y. Estimating the eigenvalues on quaternionic Kähler manifolds. International Journal of Mathematics. 2006 Jul;17(6):665-691. https://doi.org/10.1142/S0129167X06003643
Homma, Yasushi. / Estimating the eigenvalues on quaternionic Kähler manifolds. In: International Journal of Mathematics. 2006 ; Vol. 17, No. 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

VL - 17

SP - 665

EP - 691

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 6

ER -

Access to Document