Nonexistence of nontrivial 𝑐𝑚”-harmonic 1-forms on a complete foliated Riemannian manifold

Kitahara, Haruo

doi:10.1090/S0002-9947-1980-0586726-X

Nonexistence of nontrivial $cm”$-harmonic 1-forms on a complete foliated Riemannian manifold
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by Haruo Kitahara

Trans. Amer. Math. Soc. 262 (1980), 429-435

DOI: https://doi.org/10.1090/S0002-9947-1980-0586726-X

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Abstract:

We study the nonexistence of nontrivial $\square ''$-harmonic 1-forms on a complete foliated riemannian manifold with positive definite Ricci curvature. It is well known that the harmonic 1-form on a compact and orientable riemannian manifold with positive definite Ricci curvature is trivial. Our main theorem is an extension of this fact in the complete foliated riemannian case.

References

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