# Dirac eigenvalues and total scalar curvature

by

Bernd Ammann and Christian Bär

**Dirac eigenvalues and total scalar curvature**
(.dvi,
.ps,
.ps.gz oder
.pdf)

*J. Geom. Phys.* **33**, *229-234* (2000)

It has recently been conjectured that the eigenvalues
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:

We show by example that such an estimate is impossible. The example
contains a very long and thin cylinder and therefore
looks like a manifold with a very long nose.
58G25
### Keywords

eigenvalues of the Dirac operator, total scalar curvature, Pinocchio metric

Bernd Ammann, 24.6.1999