On a theorem of Chern

Sampson, J. H.

doi:10.1090/S0002-9947-1973-0317221-7

On a theorem of Chern
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Trans. Amer. Math. Soc. 177 (1973), 141-153 Request permission

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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Variétés différentiables

16

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The classical groups

1