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Geometric & Functional Analysis GAFA

, Volume 8, Issue 6, pp 965–977 | Cite as

Yamabe Invariants and $ Spin^c $ Structures

  • M.J. Gursky
  • C. LeBrun

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 \( spin^c \) 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.

Keywords

Present Method Scalar Curvature Dirac Operator Compact Manifold Lower Eigenvalue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • M.J. Gursky
    • 1
  • C. LeBrun
    • 2
  1. 1.Dept. of Math., Indiana University, Bloomington, IN 47405, USA, e-mail: gursky@indiana.eduUS
  2. 2.Dept. of Math., SUNY Stony Brook, Stony Brook, NY 11795, USA, e-mail: claude@math.sunysb.eduUS

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