A holonomy proof of the positive curvature operator theorem

Poor, W. A.

doi:10.1090/S0002-9939-1980-0567991-7

A holonomy proof of the positive curvature operator theorem
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by W. A. Poor PDF

Proc. Amer. Math. Soc. 79 (1980), 454-456 Request permission

Abstract:

Extending work of Bochner-Yano and M. Berger, D. Meyer proved that if the curvature operator of a compact, oriented, Riemannian manifold M has positive eigenvalues, then M is a rational homology sphere. Here a proof is given using Chern’s holonomy formula for the Laplacian on M; for completeness, a quick proof of Chern’s formula is included.

References

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Un théorème fondamental de Chern en géométrie riemannienne