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Zeitschrift für Analysis und ihre Anwendungen


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Volume 1, Issue 2, 1982, pp. 71–95
DOI: 10.4171/ZAA/15

Published online: 1982-04-30

Spektrale Geometrie und Huygenssches Prinzip für Tensorfelder und Differentialformen I

Rainer Schimming[1]

(1) Ernst-Moritz-Arndt-Universität Greifswald, Germany

Several Laplace operators $L$ over an $n$-dimensional Riemannian manifold ($M, g$), applying to tensor fields and (alternating or symmetric) differential forms of degree $p$, are considered. For definite $g$ and closed $M$ results on spectral geometry are obtained. If e.g. some $L$ is iso-spectral to a Laplacian of a flat manifold and $p$ greater than some bound depending on $n$, then $(M, g)$ is flat. For lorentzian $g$ and $n = 6$ results on Huygens’ principle (HP) are obtained. From $HP$ and additional assumptions there follows that $(M, g)$ is flat.

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Schimming Rainer: Spektrale Geometrie und Huygenssches Prinzip für Tensorfelder und Differentialformen I. Z. Anal. Anwend. 1 (1982), 71-95. doi: 10.4171/ZAA/15