Spectre du laplacien sur les formes versus spectre des volumes : le cas des grassmanniennes
Thèses d'Orsay, no. 574 (2000) , 166 p. 
@phdthesis{BJHTUP11_2000__0574__P0_0,
     author = {El Chami, Fida},
     title = {Spectre du laplacien sur les formes versus spectre des volumes : le cas des grassmanniennes},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud U.F.R. Scientifique d'Orsay},
     number = {574},
     year = {2000},
     language = {fr},
     url = {http://archive.numdam.org/item/BJHTUP11_2000__0574__P0_0/}
}
TY  - BOOK
AU  - El Chami, Fida
TI  - Spectre du laplacien sur les formes versus spectre des volumes : le cas des grassmanniennes
T3  - Thèses d'Orsay
PY  - 2000
IS  - 574
PB  - Université de Paris-Sud U.F.R. Scientifique d'Orsay
UR  - http://archive.numdam.org/item/BJHTUP11_2000__0574__P0_0/
LA  - fr
ID  - BJHTUP11_2000__0574__P0_0
ER  - 
%0 Book
%A El Chami, Fida
%T Spectre du laplacien sur les formes versus spectre des volumes : le cas des grassmanniennes
%S Thèses d'Orsay
%D 2000
%N 574
%I Université de Paris-Sud U.F.R. Scientifique d'Orsay
%U http://archive.numdam.org/item/BJHTUP11_2000__0574__P0_0/
%G fr
%F BJHTUP11_2000__0574__P0_0
El Chami, Fida. Spectre du laplacien sur les formes versus spectre des volumes : le cas des grassmanniennes. Thèses d'Orsay, no. 574 (2000), 166 p. http://numdam.org/item/BJHTUP11_2000__0574__P0_0/

[1] B. L. Beers and R. S. Millman : The spectra of the Laplace-Beltrami operator on compact, semisimple Lie groups, Amer. J. Math. 99 (1977), 801-807. | MR | Zbl | DOI

[2] P. Bérard : Spectral Geometry, Direct and Inverse Problems, LNM 1207, Springer, Berlin, 1986. | MR | Zbl

[3] P. Bérard : Transplantation et isospectralité II, J. London Math. Soc. (2) 48, No. 3 (1993), 565-576. | MR | Zbl | DOI

[4] P. Bérard, H. Pesce : Construction de variétés isospectrales autour du théorème de T. Sunada, Progress in inverse spectral geometry, Basel : Birkhaeuser (1997), 63-83. | MR | Zbl

[5] M. Berger, P. Gauduchon et E. Mazet : Le spectre d'une variété riemannienne, LNM 194, Springer, Berlin, 1971. | Zbl

[6] N. Bourbaki : Groupes et algèbres de Lie, Chapitre 9, Masson, Paris, 1982. | MR | Zbl

[7] T. Bröcker and T. Tom Dieck : Representations of Compact Lie Groups, Graduate Texts in Mathematics 98, Springer-Verlag, New York, 1985. | MR | Zbl

[8] P. Buser : Geometry and Spectra of Compact Riemann Surfaces, Birkhauser, Basel, 1992. | MR | Zbl

[9] I. Chavel : Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984. | MR | Zbl

[10] J. Chazarain : Formule de Poisson pour les variétés riemanniennes, Inventiones Math. 24 (1974), 65-82. | MR | Zbl | DOI

[11] S. S. Chern, M. Do Carmo and S. Kobayashi : Minimal submanifolds of a sphere with second fundamental form of constant length, Funct. Anal. Relat. Fields, Conf. Chicago 1968, (1970), 59-75. | MR | Zbl

[12] Y. Colin De Verdière : Spectre du laplacien et longueurs des géodésiques périodiques I et II, Compositio Math. 27 (1973), 83-106 et 159-184. | MR | Zbl | Numdam

[13] D. M. Deturck, C. S. Gordon : Isospectral deformations. II : Trace formulas, metrics, and potentials, Commun. Pure Appl. Math. 42, No.8 (1989), 1067-1095. | MR | Zbl | DOI

[14] D. M. Deturck, H. Gluck, C. S. Gordon, D. Webb : How can a drum change shape, while sounding the same ?, Differential Geometry, Pitman Monogr. Surv. Pure Appl. Math. 52 (1991), 111-122. | MR | Zbl

[15] D. M. Deturck, H. Gluck, C. S. Gordon, D. Webb : How can a drum change shape, while sounding the same ? II, Mechanics, analysis and geometry : 200 years after Lagrange (1991), 335-358. | MR | Zbl

[16] D. M. Deturck, H. Gluck, C. S. Gordon, D. Webb : The inaudible geometry of nilmanifolds, Invent. Math. 111, No.2 (1993), 271-284. | MR | Zbl | DOI

[17] J. Duistermaat and V. Guillemin : The spectrum of positive elliptic operators and periodic bicharacteristics, Inventiones Math. 29 (1975), 39-79. | MR | Zbl | DOI

[18] W. Fulton and J. Harris : Representation Theory, A First Course, Graduate Texts in Mathematics 129, Springer-Verlag, New York, 1991. | MR | Zbl

[19] S. Gallot, D. Hulin and J. Lafontaine : Riemannian Geometry, Springer-Verlag, Berlin Heidelberg, 1993.

[20] S. Gallot et D. Meyer : Opérateur de courbure et Laplacien des formes différentielles d'une variété riemannienne, J. Math. Pure Appl. 54 (1975), 259-284. | MR | Zbl

[21] C. S. Gordon : The Laplace spectra versus the length spectra of Riemannian manifolds, Nonlinear problems in geometry, Proc. AMS Spec. Sess., 820th Meet. AMS, Contemp. Math. 51 (1986) 63-80. | MR | Zbl | DOI

[22] R. Gornet : The marked length spectrum vs the Laplace spectrum on forms on Riemannian nilmanifolds, Comment. Math. Helv. 71, No.2 (1996), 297-329. | MR | Zbl | DOI

[23] S. Helgason : Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. | MR | Zbl

[24] J. I. Humphreys : Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics 9, Springer-Verlag, New York, 1972. | MR | Zbl

[25] A. Ikeda : On the spectrum of a Riemannian manifold of positive constant curvature I and II, Osaka J. Math. 17 (1980), 75-93 and 691-702. | MR | Zbl

[26] A. Ikeda : On lens spaces which are isospectral but not isometric, Ann. scient. Ec. Norm. Sup. 4e série, t. 13 (1980), 303-315. | MR | Zbl | Numdam | DOI

[27] A. Ikeda : On spherical space forms which are isospectral but not isometric, J. Math. Soc. Japan 35 (1983), 437-444. | MR | Zbl | DOI

[28] A. Ikeda : Riemannian manifolds p-isospectral but not (p+1)-isospectral, Coll. Pap. 35th Symp. Diff. Geom., Matsumoto/Japan 1988, Perspect. Math. 8 (1989), 383-417. | MR | Zbl

[29] A. Ikeda : On space forms of real Grassmann manifolds which are isospectral but not isometric, Kodai Math. J. 20 (1997), 1-7. | MR | Zbl | DOI

[30] A. Ikeda and Y. Taniguchi : Spectra and eigenforms of the Laplacian on S n and P n ( C ) , Osaka J. Math. 15 (1978), 515-546. | MR | Zbl

[31] A. Ikeda and Y. Yamamoto : On the spectra of 3-dimensional lens spaces, Osaka J. Math. 16 (1979), 447-469. | MR | Zbl

[32] J. Jost : Riemannian Geometry and Geometric Analysis, Springer-Verlag, Berlin Heidelberg, 1995. | MR | Zbl | DOI

[33] E. Kaneda : The spectra of 1-forms on simply connected compact irreducible Riemannian symmetric spaces, J. Math. Kyoto Univ. 23 (1983), 369-395. | MR | Zbl

[34] E. Kaneda : The spectra of 1-forms on simply connected compact irreducible Riemannian symmetric spaces II, J. Math. Kyoto Univ. 24 (1984), 141-162. | MR | Zbl

[35] H. B. Lawson, Jr. : Local rigidity theorems for minimal hypersurfaces, Ann. of Math. 89 (1969), 187-197. | MR | Zbl | DOI

[36] H. Marbes : On the spectra of compact locally symmetric Riemannian manifolds, Math. Nachr. 104 (1981), 83-99. | MR | Zbl | DOI

[37] Y. Matsushima and S. Murakami : On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Ann. of Math. 78 (1963), 365-413. | MR | Zbl | DOI

[38] A. L. Onishchik and E. B. Vinberg : Lie Groups and Lie Algebras III, Springer-Verlag, Berlin Heidelberg, 1994. | Zbl

[39] L. Paquet : Méthode de séparation des variables et calcul du spectre d'opérateurs sur les formes différentielles, Bull. Sc. Math., 2° série 105 (1981), 85-112. | MR | Zbl

[40] T. Sunada : Riemannian coverings ans isospectral manifolds, Ann. of Math. 121 (1985), 169-186. | MR | Zbl | DOI

[41] M. Takeuchi : Lie Groups II, Translations of mathematical monographs 85, AMS, 1991. | MR | Zbl

[42] M. Takeuchi : Modern Spherical Functions, Translations of mathematical monographs 135, AMS, 1994. | MR | Zbl

[43] C. Tsukamoto : Spectra of Laplace-Beltrami operators on S O ( n + 2 ) / S O ( 2 ) × S O ( n ) and S p ( n + 1 ) / S p ( 1 ) × S p ( n ) , Osaka J. Math. 18 (1981), 407-426. | MR | Zbl

[44] M. F. Vignéras : Variétés riemanniennes isospectrales et non isométriques, Ann. of Math. 112 (1980), 21-32. | MR | Zbl | DOI

[45] J. A. Wolf : Spaces of constant curvature, Publish or Perish, Boston, 1984. | MR | Zbl