Locally non-isometric yet super isospectral spaces

Geometric and Functional Analysis

Volumn 9, Issue 1, 1999, Pages 185-214

  Szabo Z I ^a,b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b RESEARCH INSTITUTE FOR TECHNICAL PHYSICS AND MATERIALS SCIENCE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033415932     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390050084     Document Type: Article

References (29)

1. A.L. BESSE, Manifolds all of whose Geodesics are Closed, Springer-Verlag, Berlin, 1987.
2. R. BROOKS, R. TSE, Isospectral surfaces of small genus, Nagoya Math. J. 107 (1987), 13-24.
3. P. BUSER, Isospectral Riemann surfaces, Ann. Inst. Fourier (Grenoble) 36 (1986), 167-192.
4. I. CHAVEL, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
5. R. COURANT, D. HILBERT, Methods of Mathematical Physics, Vol. I, Interscience, 1953.
6. M. COWLING, A.H. DOOLEY, A. KORANYI, F. RICCI, H-type groups and Iwasawa decompositions, Adv. in Math. 87 (1991), 1-41.
7. E. DAMEK, Geometry of a semidirect extension of a Heisenberg type nilpotent group, Colloq. Math. 53 (1987), 255-268.
8. E. DAMEK, F. RICCI, A class of non-symmetric harmonic manifolds, Bull. Amer. Math. Soc. 27 (1992), 139-142.
9. E. DAMEK, F. RICCI, Harmonic analysis on solvable extensions of H-type groups, preprint.
10. D. DE'TRUCK, C. GORDON, Isospectral deformations II, Comm. Pure Appl. Math. 42 (1989), 1067-1095.
11. J. DODZIUK, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math. J. 32 (1983), 703-716.
12. C. GORDON, Isospectral closed Riemannian manifolds which are not locally isometric, J. Diff. Geom. 37 (1993), 639-649.
13. C. GORDON, Isospectral closed manifolds which are not locally isometric, II, in "Contemporary Mathematics: Geometry of the Spectrum" (R. Brooks, C. Gordon, P. Perry) AMS 173 (1994), 121-131.
14. C. GORDON, D. WEBB, S. WOLPERT, One can not hear the shape of a drum, Bull. Amer. Math. Soc. 27:1 (1992), 134-138.
15. C. GORDON, E.N. WILSON, Isospectral deformations of compact solvmanifolds, J. Diff. Geom. 19 (1984), 241-256.
16. C. GORDON, E.N. WILSON, The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J. 33 (1986), 253-271.
17. C. GORDON, E.N. WILSON, Continuous families of isospectral Riemannian metrics which are not locally isometric, J. Diff. Geom. 47 (1997), 504-529.
18. A. IKEDA, On lens spaces which are isospectral but not isometric, Ann. Sci. Ecole Norm. Sup. 4:13 (1980), 303-315.
19. A. KAPLAN, Riemannian nilmanifolds attached to Clifford modules, Geom. Dedicata 11 (1981), 127-136.
20. J. MiLNOR, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A. (1964), 542. H. PESCE, Calcul du spectre d'une nilvariete de rang deux et applications, Trans. Amer. Math. Soc. 339 (1993), 433-461.
21. J. MiLNOR, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A. (1964), 542. H. PESCE, Calcul du spectre d'une nilvariete de rang deux et applications, Trans. Amer. Math. Soc. 339 (1993), 433-461.
22. F. RlCCI, Harmonic analysis on groups of H-type, preprint.
23. C. RIEHM, Explicit spin representation and Lie algebras of Heisenberg type, J. London Math. Soc. 29 (1984), 49-62.
24. R.S. STRICHARTZ, Analysis of the Laplacians on the complete Riemannian manifold, J. Punc. Anal. 52 (1983), 48-79.
25. T. SUNADA, Riemannian coverings and isospectral manifolds, Ann. of Math. 2:121 (1985), 169-186.
26. Z.I. SZABO, Lichnerowicz conjecture on harmonic manifolds, J. Diff. Geom. 31 (1990), 1-28.
27. Z.I. SZABÓ, Spectral theory for operator families on Riemannian manifolds, in "Proc. of Symp in Pure Math." Part 3, 54 (1993), 615-665.
28. M.-F. VIGNERAS, Varietes Riemanniennes isospectrales et non isometrique, Ann. of Math. 2:112 (1980), 21-32.
29. S.T. YAU, On the heat kernel of a complete Riemannian manifold, J. Math. Pure Appl. 9:57 (1978), 191-201.