New lower bound for eigenvalues of the Dirac operator

  • Georges Habib (MPI MiS Leipzig)
A3 01 (Sophus-Lie room)


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 $E^\psi$ of the tangent bundle associated with an eigenspinor $\psi$. We then show that, for isometric immersions and Riemannian flows (local Riemannian submersions), the limiting case could be achieved. In this case the tensor $E^\psi$ is identified with the second fundamental form of the immersion while it is identified with the O'Neill tensor of the flow.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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