Erratum to: Concordance and Isotopy of Metrics with Positive Scalar Curvature

Abstract

If (W, g) is a connected Riemannian manifold with a boundary (∂W, g) such that (a) Rg ≡ 0 on W , (b) ∫ ∂W hg dσg > 0, where g = g|∂W . Then the conformal manifold (W, [g]) cannot be of a zero conformal class. This statement is false. Indeed, in this case the first eigenvalue μ1 coincides with a minimum of the Rayleigh quotient ∫ W an|∇gf |2 dσg + 2(n− 1) ∫ ∂W hgf 2 dσg ∫ ∂W f 2 dσg , f ≡ 0. (1)