Dirac eigenvalues and total scalar curvature

Autoren: Bernd Ammann, Christian Bär (2000)

It has recently been conjectured that the eigenvalues λ of the Dirac operator on a closed Riemannian spin manifold M of dimension n ≥ 3 can be estimated from below by the total scalar curvature:

<tex>\lambda^2\geq\frac{n}{4(n-1)}\cdot\frac{\int_{M} S}{vol(M)}</tex>

We show by example that such an estimate is impossible.

Zeitschrift:
J. Geom. Phys.
Verlag:
Elsevier
Seiten:
229-234
Band:
33, no.3-4

zur Übersicht der Publikationen