Abstract
We show a lower bound of the L n/2-norm of the Weyl tensor in terms of the Yamabe invariant if M n has Betti number b n/2>0. This is a counterpart to a result by Akutagawa, Botvinnik, Kobayashi, and Seshadri, who proved that the L n/2-norm of the Weyl tensor can be arbitrarily large for conformal classes whose Yamabe invariant is close to the sigma invariant.
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Listing, M. L n/2-Curvature Gaps of the Weyl Tensor. J Geom Anal 24, 786–797 (2014). https://doi.org/10.1007/s12220-012-9356-7
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DOI: https://doi.org/10.1007/s12220-012-9356-7