Spektrale Geometrie und Huygenssches Prinzip für Tensorfelder und Differentialformen I
Rainer Schimming
Ernst-Moritz-Arndt-Universität Greifswald, Germany
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Abstract
Several Laplace operators over an -dimensional Riemannian manifold (), applying to tensor fields and (alternating or symmetric) differential forms of degree , are considered. For definite and closed results on spectral geometry are obtained. If e.g. some is iso-spectral to a Laplacian of a flat manifold and greater than some bound depending on , then is flat. For lorentzian and results on Huygens’ principle (HP) are obtained. From and additional assumptions there follows that is flat.
Cite this article
Rainer Schimming, Spektrale Geometrie und Huygenssches Prinzip für Tensorfelder und Differentialformen I. Z. Anal. Anwend. 1 (1982), no. 2, pp. 71–95
DOI 10.4171/ZAA/15