## By THOMAS FRIEDRICH of Berlin (Eingegangen am 9.9. 1980) Let M\* he a cony'act RIEMANNian spin inanifold with positive scalar curvature H and let R, denote its minimum. Consider the DIRAC operator D : r ( S ) + r ( S ) acting on sections of the associated spinor bundle S. If I.\* is the first p
On the first eigenvalue of the Dirac operator on 6-dimensional manifolds
β Scribed by Thomas Friedrich; Ralf Grunewald
- Publisher
- Springer
- Year
- 1985
- Tongue
- English
- Weight
- 228 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0232-704X
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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.
## Abstract For eigenvalues of generalized Dirac operators on compact Riemannian manifolds, we obtain a general inequality. By using this inequality, we study eigenvalues of generalized Dirac operators on compact submanifolds of Euclidean spaces, of spheres, and of real, complex and quaternionic pr
In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface M 2 ~ ~3 as well as intrinsic bounds for two-dimensional compact manifolds of genus zero and genus one. Moreover, we compare the different estimates of the eigenvalue