Preprint
Inserted: 6 nov 2026
Last Updated: 6 nov 2026
Pages: 35
Year: 2026
Doi: 10.5281/zenodo.23984805
Notes:
Version v1. First published on 5 November 2026.
2020 Mathematics Subject Classification: Primary 58J53; Secondary 53C22, 53C26, 53C55.
Links: Zenodo record (v1), Author's page
Abstract:
The ordinary one-form spectrum determines the standard spheres, real, complex and quaternionic projective spaces, and the Cayley plane among closed connected Riemannian manifolds. The same conclusion holds in the complementary degree without an orientability assumption; for the complex projective plane it holds in each degree $0 \leq p \leq 4$. Above dimension four, partial spectral matchings suffice in degree one and in the complementary degree under quantitative bounds on omitted eigenvalue copies and matching cost. In sufficiently large dimension, a matching after independent finite omissions with error $o(\nu^{-1})$, uniformly as the model eigenvalue $\nu \to \infty$, determines every $d$-dimensional model in a common set of form degrees. As $d \to \infty$, the lower limit of their proportion among $0,\ldots,d$ is at least $\sqrt{8/21}$. Heat identities and geodesic returns give averaged curvature bounds; for nonreal projective targets of dimension greater than four, equality in a periodic index estimate then determines the Jacobi operators.
Keywords: Hodge Laplacian, inverse spectral geometry, compact rank-one symmetric space, periodic geodesic flow
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