Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ballmann, W. On the construction of isospectral manifolds, preprint, (2000).
Brooks, R. On manifolds of negative curvature with isospectral potentials,Topology,26, 63–66, (1987).
Brooks, R. and Gordon, C.S. Isospectral families of conformally equivalent Riemannian metrics,Bull. Am. Math. Soc.,23(3), 433–436, (1990).
Brooks, R., Gornet, R. and Gustafson, W.H. Mutually isospectral Riemann surfaces,Adv. Math.,138, 306–322, (1998).
Brooks, R., Perry, P., and Yang, P. Isospectral sets of conformally equivalent metrics,Duke Math. J.,58, 131–150, (1989).
DeTurck, D. and Gordon, C. Isospectral deformations II: trace formulas, metrics, and potentials,Comm. Pure Appl. Math.,42, 1067–1095, (1989).
Gardner, C.S., Greene, J.M., Kruskal, M.D., and Miura, R.M. A method for solving the Korteveg de Vries equation,Phys. Rev. Letters,19, 1095–1097, (1967).
Gilkey, P. Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian,Compositio Math. 38, 201–240, (1979).
Gordon, C.S. Isospectral closed Riemannian manifolds which are not locally isometric: II,Geometry of the Spectrum. Brooks, R., Gordon, C., and Perry, P., Eds.Contemp. Math., AMS,173, 121–131, (1994).
Gordon, C.S. Survey of isospectral manifolds,Handbook of Differential Geometry, Dillen, F.J.E. and L.C.A. Verstraelen, L.C.A., Eds., 1, Elsevier, 747–778, (2000).
Gordon, C., Gornet, R., Schueth, D., Webb, D., and Wilson, E. Isospectral deformations of closed Riemannian manifolds with different scalar curvature,Ann. Inst. Fourier,48(2), 593–607, (1998).
Gordon, C.S. and Szabo, Z.I. Isospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric,Duke Math. J.,113(2), 355–383, (2002).
Gordon, C., Webb, D., and Wolpert, S. Isospectral plane domains and surfaces via Riemannian orbifolds,Invent. Math.,110, 1–22, (1992).
Gordon, C. and Wilson, E.N. Isospectral deformations of compact solvmanifolds,J. Diff. Geom. 19, 241–256, (1984).
Gordon, C. and Wilson, E.N. Continuous families of isospectral Riemannian metrics which are not locally isometric,J. Diff. Geom.,47, 504–529, (1997).
Gornet, R. A new construction of isospectral Riemannian nilmanifolds with examples,Michigan Math. J.,43(1), 159–188, (1996).
Gornet, R. Continuous families of Riemannian manifolds isospectral on functions but not on 1-forms,J. Geom. Anal.,10(2), 281–298, (2000).
Ikeda, A. Isospectral problem for spherical space forms,Spectra of Riemannian Manifolds, Berger, M., Murakami, S., and Ochiai, T., Eds., Kaigai Publications, 57–63, (1983).
Ikeda, A. Riemannian manifoldsp-isospectral but not (p+1)-isospectral,Geometry of Manifolds (Matsumoto), Perspect. Math., Academic Press, Boston, MA,8, 383–417, (1989).
Miatello, R. and Rosseti, J.P. Flat manifolds isospectral onp-forms,J. Geom. Anal.,11, 649–667, (2001).
Miatello, R. and Rosseti, J.P. Comparison of twistedp-form spectra for flat manifolds with diagonal holonomy,Ann. Global Anal. Geom.,21(4), 341–376, (2002).
Miatello, R. and Rosseti, J.P. Length spectra andp-spectra of compact flat manifolds, preprint, (2003), math.DG/0110325.
Milnor, J. Eigenvalues of the Laplace operator on certian manifolds,Proc. Nat. Acad. Sci. USA,51, 542, (1964).
Ochiai, T. and Takahashi, T. The group of isometries of a left invariant Riemannian metric on a Lie group,Math. Ann.,223, 91–96, (1976).
Pesce, H., Représentations relativement équivalentes et variétés Riemanniennes isospectrales,C.R. Acad. Sci. Paris Série I,3118, 657–659, (1994).
Pesce, H. Quelques applications de la théorie des représentations en géométrie spectrale,Rend. Mat., Série VII,18, 1–63, (1998).
Pöschel, J. and Trubowitz, E.Inverse Spectral Theory, Pure and Applied Mathematics, vol. 130, Academic Press, (1987).
Schueth, D. Continuous families of isospectral metrics on simply connected manifolds,Ann. of Math. (2),149(1), 287–308, (1999).
Schueth, D. Isospectral manifolds with different local geometries,J. Reine Angew. Math.,534, 41–94, (2001).
Schueth, D. Isospectral metrics on five-dimensional spheres,J. Diff. Geometry,58(1), 87–111, (2001).
Spivak, M.Differential Geometry III. Publish or Perish, (1975).
Sutton, C. Isospectral simply connected homogeneous spaces and the spectral rigidity of group actions,Comment. Math. Helv.,77(4), 701–717, (2002).
Szabo, Z.I. Locally non-isometric yet super isospectral spaces,Geom. Funct. Anal.,9(1), 185–214, (1999).
Szabo, Z.I. Isospectral pairs of metrics constructed on balls, spheres, and other manifolds with different local geometries,Ann. of Math. (2),154(2), 437–475, (2001).
Szabo, Z.I. Cornucopia of isospectral pairs of metrics on balls and spheres with different local geometries, preprint, (2000), math. DG/0011034.
Urakawa, U. Bounded domains which are isospectral but not congruent,Ann. Scient. Éc. Norm. Sup.,15, 441–456, (1982).