The First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces
β Scribed by Jean-Louis Milhorat
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 168 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
On a foliated Riemannian manifold with a transverse spin structure, we give a lower bound for the square of the eigenvalues of the transversal Dirac operator. We prove, in the limiting case, that the foliation is a minimal, transversally Einsteinian with constant transversal scalar curvature.
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,