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The scalar curvature and the spectrum of the Laplacian of spin manifolds. (English) Zbl 0634.58036

The Dirac operator plays an important role in geometry of spin manifolds. For example, Lichnerowicz deduced the Â-genus vanishing theorem for spin manifolds of positive scalar curvature. In this note we give an upper bound of the greatest lower bound of the spectrum of the Laplacian on universal covering spaces of closed spin manifolds of nonvanishing Â-genus.
Reviewer: K.Ono

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J20 Index theory and related fixed-point theorems on manifolds
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References:

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