Lower bounds for eigenvalues of the Dirac operator on surfaces of rotation

Journal of Geometry and Physics

Volumn 31, Issue 2-3, 1999, Pages 209-216

  Kraus, Margarita ^a  

^a UNIVERSITY OF REGENSBURG   (Germany)

Author keywords

Dirac operator; Spectrum; Surface of rotation

Indexed keywords

EID: 0033196215     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(99)00006-6     Document Type: Article

References (17)

1. [1] I. Agricola, Th. Friedrich, Upper bounds for the Dirac operator on surfaces, J. Geom. Phys. 30 (1999) 1-22.
2. [2] B. Amann, C. Bär, The Dirac operator on nilmanifolds and collapsing circle bundles, Ann. Glob. Anal. Geom. 16 (1998) 221-253.
3. [3] G.E. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972.
4. [4] C. Bär, The Dirac operator on space forms of positive curvature, J. Math. Soc. Jpn. 48 (1994) 69-83.
5. [5] C. Bär, Lower eigenvalue estimates for Dirac operators, Math. Ann. 193 (1992) 39-46.
6. [6] C. Bär, Extrinsic bounds for eigenvalues of the Dirac operator, Ann. Glob. Anal. Geom. 16 (1998).
7. [7] C. Bär, Metrics with harmonic spinors GAFA, vol. 6, no. 6. 1996, pp. 899-942.
8. [8] H. Baum, An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds, Math. Zeitschrift 206 (1991) 409-422.
9. [9] M. Bordoni, Spectral estimates for Schrödinger and Dirac type operators on Riemannian manifolds, Math. Ann. 298 (1994) 693-718.
10. [10] U. Bunke, Upper bounds of small eigenvalues of the Dirac operator and Isometric immersions, Ann. Glob. Anal. Geom. 9 (1991) 211-243.
11. [11] Th. Friedrich, Dirac Operatoren in der Riemannschen Geometrie, Vieweg, Braunschweig, 1997.
12. [12] Th. Friedrich. Die Abhängigkeit des Dirac-Operators von der Spin-Struktur, Colloquium Mathematicum 48 (1) (1984) 57-62.
13. [13] Th. Friedrich. Der erste eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung, Mathematische Nachrichten 97 (1980) 117-146.
14. [14] Th. Friedrich, On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998) 143-157.
15. [15] H.-B. Lawson, M.-L. Michelson, Spin Geometry, Princeton University Press, Princeton, NJ, 1989.
16. [16] J. Lott, Eigenvalue bounds for the Dirac operator, Pac. J. Math. 125 (1986).
17. [17] S. Sulanke, Berechnung des Spektrums des Quadrates des Dirac-Operators auf der Sphäre und Untersuchung zum ersten Eigenwert von D auf 5-dimensionalen Räumen konstanter positiver Schnittkrümmung, Dissertation, Humboldt-Universität, Berlin, 1981.