ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53, 58 Friedland, Lew, state University of New York, USA Spectral geometry on almost Hermitian manifolds. The spectrum Spec^{p}(M, G) of eigenvalues of the Laplace-Beltrami operator Δ = −(dδ + δd) on the space of smooth p-forms C^{∞}(Λ^{p}(M)) on compact Riemannian and Kähler manifolds determines the geometry of the manifolds to a considerable extent, though isospectral manifolds may not be isometric. This paper continues a study of the geometric consequences of isospectrality on different classes of almost Hermitian manifolds. We begin with a summary of the earlier results and derive stronger conclusions. We then consider the implications of isospectrality on almost Hermitain manifolds with certain quite natural curvature constraints, such as constant curvature and Bochner-flat spaces.