The Dirac operator on collapsing S 1 -bundles

Bernd Ammann

Séminaire de théorie spectrale et géométrie (1997-1998)

  • Volume: 16, page 33-42
  • ISSN: 1624-5458

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Ammann, Bernd. "The Dirac operator on collapsing $S^1$-bundles." Séminaire de théorie spectrale et géométrie 16 (1997-1998): 33-42. <http://eudml.org/doc/114423>.

@article{Ammann1997-1998,
author = {Ammann, Bernd},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {spin Dirac operator; spectrum; collapsing circle bundle},
language = {eng},
pages = {33-42},
publisher = {Institut Fourier},
title = {The Dirac operator on collapsing $S^1$-bundles},
url = {http://eudml.org/doc/114423},
volume = {16},
year = {1997-1998},
}

TY - JOUR
AU - Ammann, Bernd
TI - The Dirac operator on collapsing $S^1$-bundles
JO - Séminaire de théorie spectrale et géométrie
PY - 1997-1998
PB - Institut Fourier
VL - 16
SP - 33
EP - 42
LA - eng
KW - spin Dirac operator; spectrum; collapsing circle bundle
UR - http://eudml.org/doc/114423
ER -

References

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  1. [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. [2] B. AMMANN, Spin-Strukturen und das Spektrum des Dirac-Operators, Dissertation, Universität Freiburg, ISBN 3-8265-4282-7, Shaker Verlag Aachen 1998. 
  3. [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. [4] C. BÄR, Metrics with harmonic spinors, GAFA 6, 899-942 ( 1996). Zbl0867.53037MR1421872
  5. [5] L. BÉRARD BERGERY, J.-P. BOURGUIGNON, Riemannian submersions with totally geodesic fibers, Illinois J. Math. 26, 151-200 ( 1982). Zbl0483.58021MR650387
  6. [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. [7] B. COLBOIS, J. DODZIUK, Riemannian metrics with large λ1, Proc. Amer. Math. Soc. 122 no. 3, 905-906 ( 1994). Zbl0820.58056MR1213857
  8. [8] T. FRIEDRICH, Zur Abhängigkeit des Dirac-Operators von der Spin-Strukturt, Colloq. Math. 48, 57-62 ( 1984). Zbl0542.53026MR750754
  9. [9] K. FUKAYA, Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math. 87, 517-547 ( 1987). Zbl0589.58034MR874035
  10. [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. [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. [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. [13] N. HITCHIN, Harmonic spinors, Adv. Math. 14, 1-55 ( 1974). Zbl0284.58016MR358873
  14. [14] J.-Y. WU, The topological spectrum of a smooth closed manifold, Ind. Univ. Math. J.44, no. 2, 511-534 ( 1995). Zbl0843.58124MR1355410

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