**I. Homogeneous Riemannian
manifolds**

**II. Kahler and symplectic
structures**

A. Isospectral closed manifolds with a common Riemannian covering

B. Isospectral plane or hyperbolic domains

C. Laplace spectrum versus geometry

D. Isospectral Riemannian manifolds with different local geometry

**I. Homogeneous
Riemannian manifolds**

Riemannian
isometry groups containing transitive reductive subgroups, Math. Ann. 248 (1980),
185-192.

Transitive Riemannian
isometry groups with nilpotent radicals, Ann. Inst. Fourier, Grenoble 31 (1981),
192-204.

Semisimple normal subgroups of transitive Riemannian isometry groups, Osaka
J. Math. 19 (1982), 283-286.

with E. N. Wilson, The fine structure of transitive Riemannian isometry groups,
part I, Trans. Amer. Math. Soc. 289 (1985), 367-380.

with W. Ziller, Naturally reductive metrics of non-positive Ricci curvature, Proc. Amer.
Math. Soc. 91 (1984), 287-290.

Naturally reductive homogeneous Riemannian manifolds, Canadian J. Math. 37 (1985), 467-487.

with E. N. Wilson, Isometry groups of solvmanifolds, Trans. Amer. Math. Soc. 397 (1988),
245-269.

Homogeneous Riemannian manifolds whose geodesics are orbits, in "Topics in Geometry:
Honoring the Memory of Joseph D'Atri, Birkhauser, Boston 1996, 155-174.

with M. Kerr, New examples of homogeneous Einstein manifolds, to appear in Global Analysis
and Geometry

**II. Kahler and
symplectic structures**

with C. Benson, Kahler and symplectic structures on nilmanifolds,
Topology 27 (1988), 513-518.

with C. Benson, Kahler structures on complete solvmanifolds, Proc. Amer. Math. Soc. 108
(1990), 971-980.

A. Isospectral closed manifolds with a common Riemannian covering

with E. N. Wilson, Isospectral deformations of compact solvmanifolds,
J. Diff. Geom. 19 (1984), 241-256.

The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Mich. Math. J. 33
(1986), 253-271.

Riemannian manifolds isospectral on functions but not on
1-forms, J. Diff. Geom. 24 (1986), 79-96.

with R. Brooks, Isospectral families of conformally equivalent Riemannian metrics,

Bulletin Amer. Math. Soc. 23 (1990), 433-436.

with D. DeTurck, H. Gluck, and D. Webb Isospectral conformally equivalent Riemannian
metrics, Indiana Univ. Math. J. 41 (1992), 99-107.

with D. DeTurck, Isospectral Riemannian metrics and finite coverings, Contemporary Math.
64 (1987), 79-92.

with D. DeTurck, Isospectral deformations I: Riemannian structures on two-step nilspaces,
Comm. Pure and Appl. Math. 40 (1987), 367-387.

with D. DeTurck, Isospectral deformations II: Trace formulas, metrics, and potentials,
Comm. Pure Appl. Math. 42 (1989), 1067-1096.

with D. DeTurck , Isospectral Riemannian metrics and potentials, announcement, Bull. Amer.
Math. Soc. 17, no. 1 (1987), 137-140.

with H. Ouyang and D. Schueth, Distinguishing isospectral nilmanifolds by bundle
Laplacians, Math. Research Letters 4 (1997), 23-33.

B. Isospectral plane or hyperbolic domains

with D. Webb and S. Wolpert, One can't hear the shape of a drum, Bull.
Amer. Math. Soc. 27 (1992), 134-138.

with D. Webb and S. Wolpert, Isospectral plane domains and surfaces via Riemannian
orbifolds, Invent. math. 110 (1992), 1-22.

with D. Webb, Isospectral convex domains in the hyperbolic plane, Proc. Amer. Math. Soc.

with D. Webb, Isospectral convex domains in Euclidean space,
Math. Research Letters 1 (1994), 539-545.

C. Laplace spectrum versus geometry

with D. DeTurck, H. Gluck, and D. Webb, You can't hear the size of a
homology class, Comm. Math. Helv. 64 (1989), 589-617.

with D. DeTurck, H. Gluck, and D. Webb, The inaudible geometry of nilmanifolds, Invent.
Math. 111 (1993), 271-284.

The Laplace spectra versus the length spectra of Riemannian mnaifolds, Contemporary
Mathematics 51 (1986), 63-79.

with Yiping Mao, Comparison of Laplace spectra, length spectra and geodesic flows of some
Riemannian manifolds, Math. Research Letters 1, no. 6 (1994), 677-688.

with Y. Mao, Geodesic fonjugacy on two-step nilmanifolds, Mich. Math. J..45 (1998),
451-481.

with Y. Mao and D. Schueth, Symplectic rigidity of geodesic flows on two-step
nilmanifolds, Ann. Scient. de l'Ecole Norm. Sup. 30 (1997), 417-427.

with J. P. Rossetti, Boundary volume and length spectra of Riemannian manifolds:
What the middle degree Hodge spectrum doesn't reveal, Ann. Inst. Fourier,
Grenoble 53 (2003, 2297-2314.

with E. Makover and D. Webb, Transplantation and Jacobians of Sunada isospectral
Riemann surfaces, Adv.
in Math. 197 (2005), 86-119.

D. Isospectral Riemannian manifolds with different local geometry

Isospectral Riemannian manifolds which are not locally isometric, J. Diff. Geom. 37 (1993), 639-650.

Isospectral Riemannian manifolds which are not locally isometric, II, Contemp. Math. 173 (1994), 121-132.

with E. N. Wilson, Continuous families of isospectral Riemannian manifolds which are not
locally isometric, J. Diff. Geom. 47 (1997), 504-529.

with R. Gornet, D. Schueth, D. Webb, and E. Wilson, Isospectral deformations of closed
manifolds with different scalar curvature, Ann. Inst. Fourier, Grenoble 48 (1998),
593-607.

with Z. I. Szabo, Isospectral deformations of negatively
curved Riemannian manifolds with boundary which are not locally isometric, Duke Math. J. 113 (2002), no. 2, 355-383.

Isospectral deformations of Riemannian metrics on balls and spheres, Invent. Math. 145 (2001), no. 2, 317-331.

with D. Schueth, Isospectral potentials and
conformally equivalent isospectral metrics on spheres, balls and Lie groups, J.
Geom. Anal. 13 (2003), no. 2, 300--328.

with P. Perry, Continuous families of isophasal
scattering manifolds, preprint arXiv.org/absmath.DG/0211039.

E. Isospectral potentials for the Schrodinger operator

with T. Kappeler, On isospectral separable potentials on tori, Duke
Math. J. 63 (1991), 217-233.

with T. Kappeler, On isospectral potentials on tori, II, Comm. in P.D.E. (1995)

with P. Guerini, T. Kappeler, and D. Webb,
__Inverse spectral results on even dimensional tori__,
preprint.

F. Expository articles

When you can't hear the shape of a manifold, The Mathematical
Intelligencer 11, no.3 (1989), 39-47.

You can't hear the shape of a manifold, Proceedings of Conference on Representations
of Lie Groups and Their Applications, (J. Tirao and N. Wallach, eds.), Birkhauser
1992, 129-146.

with D. Webb, You can't hear the shape of a drum, American Scientist 84 (Jan.-Feb.
1996), 46-55.

with R. Gornet, Spectral geometry of nilmanifolds, in Progress in Inverse Spectral
Geometry (S. Andersson and M. Lapidus, ed), Birkh\auser--Verlag, Basel (1997),
23-49.

Survey of isospectral manifolds, Handbook of Differential
Geometry, North-Holland, 1999.

Isospectral Manifolds with Different Local Geometry, Korean Math. J. 38 (2001),
955-970.

with P. Perry and D. Schueth, Isospectral and isoscattering manifolds: a survey
of examples, to appear in "Geometry, Spectral Theory, Groups, and Dynamics:
Proceedings in Memory of Robert Brooks," Contemporary Mathematics.