Abstract for the talk at 24.10.2007 (11:15 h)

Georges Habib (MPI MiS Leipzig)

New lower bound for eigenvalues of the Dirac operator

In this talk, we give a new estimate for the eigenvalues of the Dirac operator on a compact spin manifold in terms of an appropriate endomorphism of the tangent bundle associated with an eigenspinor . We then show that, for isometric immersions and Riemannian flows (local Riemannian submersions), the limiting case could be achieved. In this case the tensor is identified with the second fundamental form of the immersion while it is identified with the O'Neill tensor of the flow.