✦ LIBER ✦
An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form
✍ Scribed by B. Alexandrov; G. Grantcharov; S. Ivanov
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 492 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0393-0440
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✦ Synopsis
An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smallest possible eigenvalue is attained are also listed. Moreover, a complete classification of the compact odd-dimensional manifolds whose universal covering space is S"-' x Iw is given in the limiting case. All such manifolds are diffeomorphic but not necessarily isometric to S"-' x S'.