Yamabe Invariants and
$ Spin^c $ Structures |
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| Authors: | MJ Gursky C LeBrun |
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| Institution: | (1) Dept. of Math., Indiana University, Bloomington, IN 47405, USA, e-mail: gursky@indiana.edu, US;(2) Dept. of Math., SUNY Stony Brook, Stony Brook, NY 11795, USA, e-mail: claude@math.sunysb.edu, US |
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| Abstract: | The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the
manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that
of the 4-sphere. This is done by using Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Laplacian. These results dovetail perfectly
with those derived from the perturbed Seiberg–Witten equations Le3], but the present method is much more elementary in spirit.
Submitted: October 1997 |
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