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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Indices and nullities of Yang-Mills fields


Author: Hajime Urakawa
Journal: Proc. Amer. Math. Soc. 98 (1986), 475-479
MSC: Primary 58E15; Secondary 53C80, 58G30, 81E20
DOI: https://doi.org/10.1090/S0002-9939-1986-0857945-0
MathSciNet review: 857945
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Abstract: In this note, we give an upper estimate of index and nullity of every Yang-Mills field $ R$ on every principal bundle $ P$ with structure group $ G$ over a Riemannian manifold $ (M,g)$ with Ricci tensor $ \operatorname{Ric} \geqslant kg,k > 0$, in terms of $ \dim (M)$, $ \dim (G)$, $ k$, and $ {\left\Vert R \right\Vert _\infty }$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0857945-0
Keywords: Yang-Mills field, index, nullity, eigenvalue
Article copyright: © Copyright 1986 American Mathematical Society