Vanishing theorem for transverse Dirac operators on Riemannian foliations

Abstract

We obtain a vanishing theorem for the half-kernel of a transverse ${\rm Spin}\sp c$ Dirac operator on a compact manifold endowed with a transversely almost complex Riemannian foliation twisted by a sufficiently large power of a line bundle, whose curvature vanishes along the leaves and is transversely non-degenerate at any point of the ambient manifold.

18 pages

References in corpus (1)

• The Egorov theorem for transverse Dirac type operators on foliated manifolds