A note on the Lichnerowicz vanishing theorem for proper actions (Q1676070)

Let \(G\) be a locally compact group which acts on an even dimensional spin manifold \(M\) properly and cocompactly. It is proved that the index of the associated \(G\)-equivariant Dirac operator vanishes provided that \(M\) admits a \(G\)-invariant Riemannian metric of positive scalar curvature. It is based on a classical theorem of Lichnerowicz in 1963.