TY - JOUR
T1 - Estimating the eigenvalues on quaternionic Kähler manifolds
AU - Homma, Yasushi
PY - 2006/7/1
Y1 - 2006/7/1
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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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 -