EIGENVALUE ESTIMATES OF THE BASIC DIRAC OPERATOR ON A RIEMANNIAN FOLIATION

Abstract

On a foliated Riemannian manifold with a transverse spin structure, we give a lower bound of the square for the eigenvalues of the basic Dirac operator in terms of the smallest eigenvalue of the basic Yamabe operator and of the norm of an appropriate endomorphism of the normal bundle $Q$ of $\mathcal F$. We study the limiting case.