Scalar curvature estimates for \((n+ 4k)\)-dimensional spin manifolds (Q1924849)

Combining vanishing arguments with Dirac operator techniques, some sharp estimates on the scalar curvature of \((n+ 4k)\)-dimensional spin compact manifolds which admit a nonzero \(\widehat {A}\)-degree distance decreasing map into the standard sphere are established. The estimates are extended to the noncompact case provided the map is constant at infinity.