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Curvature, Harnack's inequality, and a spectral characterization of nilmanifolds
Auteur(s)
Date de parution
2003
In
Annals of Global Analysis and Geometry
Vol.
3
No
23
De la page
227
A la page
246
Résumé
For closed n-dimensional Riemannian manifolds M with almost nonnegative Ricci curvature, the Laplacian on one-forms is known to admit at most n small eigenvalues. If there are n small eigenvalues, or if M is orientable and has n - 1 small eigenvalues, then M is diffeomorphic to a nilmanifold, and the metric is almost left invariant. We show that our results are optimal for n greater than or equal to 4.
Type de publication
Resource Types::text::journal::journal article
