The Dirac operator on space forms of positive curvature

Christian BÄR

doi:10.2969/jmsj/04810069

Christian BÄR

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JOURNAL FREE ACCESS

1996 Volume 48 Issue 1 Pages 69-83

DOI https://doi.org/10.2969/jmsj/04810069

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Published: 1996 Received: March 11, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. Bär, Das Spektrum von Dirac-Operatoren, Bonner Math. Schriften, 217 (1991).
2) C. Bär, The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces, Arch. Math., 59 (1992), 65-79.
3) C. Bär, Real Killing spinors and holonomy, Comm. Math. Phys., 154 (1993), 509-521.
4) M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer, 1971.
5) T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Springer, New York-Berlin-Heidelberg-Tokyo, 1985.
6) M. Cahen, S. Gutt, L. Lemaire and P. Spindel, Killing spinors, Bull. Soc. Math. Belg., 38 (1986), 75-102.
7) A. Franc, Spin structures and Killing spinors on lens spaces, J. Geom. Phys., 4 (1987), 277-287.
8) T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Rieman-nschen Mannigfaltigkeit nichtnegative Skalarkrümmung, Math. Nachr., 97 (1980), 117-146.
9) T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Collect. Math., 48 (1984), 57-62.
10) A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math., 17 (1980), 75-93.
11) A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature II, Osaka J. Math., 17 (1980), 691-762.
12) A. Ikeda, On lens spaces which are isospectral but not isometric, Ann. Sci. École Norm. Sup., 13 (1980), 303-315.
13) A. Ikeda, On spherical space forms which are isospectral but not isometric, J. Math. Soc. Japan, 35 (1983), 437-444.
14) A. Ikeda, Riemannian manifolds p-isospectral but not (p+1)-isospectral, In Geometry of Manifolds, Academic Press, 1989, pp. 383-417.
15) H. B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton University Press, Princeton, 1989.
16) J.-P. Serre, A Course in Arithmetic, Springer-Verlag, New York-Heidelberg-Berlin, 1973.
17) S. Sulanke, Berechnung des Spektrums des Quadrates des Dirac-Operators auf der Sphäre, Thesis, Humboldt-Universität, Berlin.
18) S. Sulanke, Der erste Eigenwert des Dirac-Operators auf S⁵/Γ, Math. Nachr., 99 (1980), 259-271.
19) J. A. Wolf, Spaces of Constant Curvature, 5th ed., Publish or Perish, Wilmington, 1984.

Right : [1] C. Bär, Das Spektrum von Dirac-Operatoren, Bonner Math. Schriften, 217 (1991).
[2] C. Bär, The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces, Arch. Math., 59 (1992), 65-79.
[3] C. Bär, Real Killing spinors and holonomy, Comm. Math. Phys., 154 (1993), 509-521.
[4] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., 194, Springer, 1971.
[5] T. Bröcker and T. tom Dieck, Representations of Compact Lie Groups, Springer, New York-Berlin-Heidelberg-Tokyo, 1985.
[6] M. Cahen, S. Gutt, L. Lemaire and P. Spindel, Killing spinors, Bull. Soc. Math. Belg., 38 (1986), 75-102.
[7] A. Franc, Spin structures and Killing spinors on lens spaces, J. Geom. Phys., 4 (1987), 277-287.
[8] T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegative Skalarkrümmung, Math. Nachr., 97 (1980), 117-146.
[9] T. Friedrich, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Collect. Math., 48 (1984), 57-62.
[10] A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature, Osaka J. Math., 17 (1980), 75-93.
[11] A. Ikeda, On the spectrum of a Riemannian manifold of positive constant curvature II, Osaka J. Math., 17 (1980), 691-762.
[12] A. Ikeda, On lens spaces which are isospectral but not isometric, Ann. Sci. École Norm. Sup., 13 (1980), 303-315.
[13] A. Ikeda, On spherical space forms which are isospectral but not isometric, J. Math. Soc. Japan, 35 (1983), 437-444.
[14] A. Ikeda, Riemannian manifolds p-isospectral but not (p+1)-isospectral, In Geometry of Manifolds, Academic Press, 1989, pp. 383-417.
[15] H. B. Lawson and M. -L. Michelsohn, Spin Geometry, Princeton University Press, Princeton, 1989.
[16] J. -P. Serre, A Course in Arithmetic, Springer-Verlag, New York-Heidelberg-Berlin, 1973.
[17] S. Sulanke, Berechnung des Spektrums des Quadrates des Dirac-Operators auf der Sphäre, Thesis, Humboldt-Universität, Berlin.
[18] S. Sulanke, Der erste Eigenwert des Dirac-Operators auf S⁵/Γ, Math. Nachr., 99 (1980), 259-271.
[19] J. A. Wolf, Spaces of Constant Curvature, 5th ed., Publish or Perish, Wilmington, 1984.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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