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- W2952340889 abstract "We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on $p$-forms, we determine all $p$-isospectral and $L$-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on $p$-forms for all values of $p$ are equivalent to each other. The list shows for any $p$, $1 le p le 3$, many $p$-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, $p$-isospectral for all $p$ and not length isospectral." @default.
- W2952340889 created "2019-06-27" @default.
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- W2952340889 date "2005-05-23" @default.
- W2952340889 modified "2023-10-01" @default.
- W2952340889 title "Spectral properties of 4-dimensional compact flat manifolds" @default.
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