Lower bounds for the eigenvalues of the Dirac operator. I: The hypersurface Dirac operator (Q5943917)

The authors establish optimal lower bounds for the hypersurface Dirac operator by using the Yamabe number, the energy-momentum tensor, and the mean curvature. In the limiting case, they prove that the hypersurface is an Einstein manifold with constant mean curvature. Contents include: an introduction; the hypersurface Dirac operator; conformal lower bounds of eigenvalues; generalized conformal lower bounds; and the energy-momentum tensor.