On lens spaces which are isospectral but not isometric

Akira Ikeda

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 3, page 303-315
  • ISSN: 0012-9593

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Ikeda, Akira. "On lens spaces which are isospectral but not isometric." Annales scientifiques de l'École Normale Supérieure 13.3 (1980): 303-315. <http://eudml.org/doc/82053>.

@article{Ikeda1980,
author = {Ikeda, Akira},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Laplacian; generating function; homotopy equivalent; isospectral non- isometric lens spaces},
language = {eng},
number = {3},
pages = {303-315},
publisher = {Elsevier},
title = {On lens spaces which are isospectral but not isometric},
url = {http://eudml.org/doc/82053},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Ikeda, Akira
TI - On lens spaces which are isospectral but not isometric
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 3
SP - 303
EP - 315
LA - eng
KW - Laplacian; generating function; homotopy equivalent; isospectral non- isometric lens spaces
UR - http://eudml.org/doc/82053
ER -

References

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  1. [1] M. BERGER, P. GAUDACHON and E. MAZET, Le spectre d'une variété riemannienne (Lecture Notes in Math., No. 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971). Zbl0223.53034MR43 #8025
  2. [2] M. M. COHEN, A Course in Simple-Homotopy Theory, Graduate Texts in Mathematics, Vol. 10, Springer-Verlag, New York-Heidelberg-Berlin, 1970. Zbl0261.57009MR43 #1195
  3. [3] G. DE RHAM, S. MAUMARY and M. A. KERVAIRE, Torsion et type simple d'homotopie (Lecture Notes in Math., No. 48, Springer-Verlag, Berlin-Heidelberg-New York, 1967). Zbl0153.53901MR36 #5943
  4. [4] N. EJIRI, A Construction of Non-Flat, Compact Irreducible Riemannian Manifolds Which are Isospectral but not Isometric (Math. Z., Vol. 212, 1979, pp. 207-212). Zbl0396.53022MR80h:58050
  5. [5] G. H. HARDY and E. M. WRIGHT, An Introduction to the Theory of Numbers, Oxford Univ. Press, 1960. Zbl0086.25803
  6. [6] A. IKEDA and Y. YAMAMOTO, On the Spectra of 3-Dimensional Lens Spaces (Osaka J. Math., Vol. 16, 1979, pp. 447-469). Zbl0415.58018MR80e:58042
  7. [7] A. IKEDA, On the Spectrum of a Riemannian Manifold of Positive Constant Curvature (Osaka J. Math., Vol. 17, 1980, pp. 75-93). Zbl0436.58025MR81a:58054
  8. [8] A. IKEDA, On the Spectrum of a Riemannian Manifold of Positive Constant Curvature. II (to appear). Zbl0451.58038
  9. [9] J. MILNOR, Eigenvalues of the Laplace Operator on Certain Manifolds (Proc. Nat. Sc. U.S.A., Vol. 51, 1964, p. 542). Zbl0124.31202MR28 #5403
  10. [10] D. B. RAY, Reidemeister Torsion and the Laplacien on Lens Spaces (Advances in Math., Vol. 4, 1970, pp. 109-126). Zbl0204.23804MR41 #2709
  11. [11] M. TANAKA, Compact Riemannian Manifolds which are Isospectral to Three Dimensional Lens Spaces. II (Proc. Fac. Sc. Tokai Univ., Vol. XIV, 1978, pp. 11-34). Zbl0436.53046MR81f:58044b
  12. [12] S. TANNO, Eigenvalues of the Laplacian of Riemannian Manifolds (Tôhoku Math. J., Vol. 25, 1973, pp. 391-403). Zbl0266.53033MR48 #12405
  13. [13] M. F. VIGNÉRAS, Exemples de sous-groupes discrets non conjugués de PSL (2, R) qui ont même fonction zêta de Selberg (C.R. Acad. Sc., T. 287, série A, 1978, pp. 47-49). Zbl0387.10013MR58 #10826
  14. [14] Y. YAMAMOTO, On the Number of Lattice Points in the Square |x| + |y| ≦ u with a Certain Congruence Condition (Osaka J. Math., Vol. 17, 1980, pp. 9-21). Zbl0426.10028MR81c:10062

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