Citation
B. Ammann et C. Bar, Dirac eigenvalues and total scalar curvature, J GEOM PHYS, 33(3-4), 2000, pp. 229-234
Citations number
10
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF GEOMETRY AND PHYSICS
ISSN journal
03930440
→ ACNP
Volume
33
Issue
3-4
Year of publication
2000
Pages
229 - 234
Database
ISI
SICI code
0393-0440(200004)33:3-4<229:DEATSC>2.0.ZU;2-I
Abstract
It has recently been conjectured that the eigenvalues lambda of the Dirac o
perator on a closed Riemannian spin manifold M of dimension n greater than
or equal to 3 can be estimated from below by the total scalar curvature:
lambda(2) greater than or equal to n <(4(n - 1))over bar> . integral(M)(S)
<(vol (M))over bar> .
We show by example that such an estimate is impossible. (C) 2000 Elsevier S
cience B.V. All rights reserved.