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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On a theorem of Chern

Author: J. H. Sampson
Journal: Trans. Amer. Math. Soc. 177 (1973), 141-153
MSC: Primary 53C10
MathSciNet review: 0317221
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Abstract: A new proof is given for Chern's theorem showing that the Laplace operator for differential forms commutes with decomposition of forms associated with G-structures admitting a suitable connection. An analogous result is proved for symmetric tensor fields, and an application is made to determine all harmonic symmetric fields on a compact space of constant negative curvature. Vector-valued forms are also discussed.

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Keywords: Laplace operator, G-structure, harmonic forms, Killing fields, symmetric fields, orthogonal group
Article copyright: © Copyright 1973 American Mathematical Society