Lower bounds for the eigenvalue of the transversal Dirac operator on a Kähler foliation (Q1864944)

The authors consider a foliated Riemann manifold with a Kähler spin foliation and give a lower bound for the square of the eigenvalues of the transversal Dirac operator (which, if the foliation is a point foliation, simply reduces to the Dirac operator on a Kähler manifold). In the case the lower bound is attained and its square root is itself an eigenvalue of the transversal Dirac operator, the Kähler foliation is minimal, transversally Einsteinian of odd complex dimension with nonnegative constant transversal scalar curvature.