The Dirac operator on collapsing -bundles
Séminaire de théorie spectrale et géométrie (1997-1998)
- Volume: 16, page 33-42
- ISSN: 1624-5458
Access Full Article
topHow to cite
topReferences
top- [1] I. AGRICOLA, B. AMMANN, T. FRIEDRICH, A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. Preprint 1998. Zbl0944.58022
- [2] B. AMMANN, Spin-Strukturen und das Spektrum des Dirac-Operators, Dissertation, Universität Freiburg, ISBN 3-8265-4282-7, Shaker Verlag Aachen 1998.
- [3] B. AMMANN, C. BÄR, The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles, Ann. Global Anal. Geom. 16, 221-253 ( 1998). Zbl0911.58037MR1626659
- [4] C. BÄR, Metrics with harmonic spinors, GAFA 6, 899-942 ( 1996). Zbl0867.53037MR1421872
- [5] L. BÉRARD BERGERY, J.-P. BOURGUIGNON, Riemannian submersions with totally geodesic fibers, Illinois J. Math. 26, 151-200 ( 1982). Zbl0483.58021MR650387
- [6] B. COLBOIS, G. COURTOIS, Convergence de variétés et convergence du spectre du Laplacien, Ann. Sc. Ec. Norm. Sup. 4e série 24, 507-518 ( 1991). Zbl0754.58040MR1123559
- [7] B. COLBOIS, J. DODZIUK, Riemannian metrics with large λ1, Proc. Amer. Math. Soc. 122 no. 3, 905-906 ( 1994). Zbl0820.58056MR1213857
- [8] T. FRIEDRICH, Zur Abhängigkeit des Dirac-Operators von der Spin-Strukturt, Colloq. Math. 48, 57-62 ( 1984). Zbl0542.53026MR750754
- [9] K. FUKAYA, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math. 87, 517-547 ( 1987). Zbl0589.58034MR874035
- [10] P.B. GILKEY, J.H. PARK, Eigenvalues of the Laplacian and Riemannian submersions,Yokohama Math. J. 43 no. 1, 7-11 ( 1995). Zbl0853.58107MR1363013
- [11] P.B. GILKEY, J.H. PARK, Riemannian submersions which preserve the eigenforms of the Laplacian, III. J. Math. 40, 194-201 ( 1996). Zbl0855.58059MR1398089
- [12] P.B. GILKEY, J.V. LEAHY, J.H. PARK, Eigenvalues of the form valued Laplacian for Riemannian submersions, Proc. Amer. Math. Soc. 126 no. 6,1845-1850 ( 1998). Zbl0903.58061MR1485476
- [13] N. HITCHIN, Harmonic spinors, Adv. Math. 14, 1-55 ( 1974). Zbl0284.58016MR358873
- [14] J.-Y. WU, The topological spectrum of a smooth closed manifold, Ind. Univ. Math. J.44, no. 2, 511-534 ( 1995). Zbl0843.58124MR1355410