Mathematics – Differential Geometry
Scientific paper
1995-10-13
Mathematics
Differential Geometry
Scientific paper
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the same marked length spectrum, they necessarily share the same Laplace spectrum on functions. In contrast, we present the first example of a pair of isospectral Riemannian manifolds with the same marked length spectrum but not the same spectrum on one-forms. Outside of the standard spheres vs. the Zoll spheres, which are not even isospectral, this is the only example of a pair of Riemannian manifolds with the same marked length spectrum, but not the same spectrum on forms. This partially extends and partially contrasts the work of Eberlein, who showed that on two-step nilmanifolds, the same marked length spectrum implies the same Laplace spectrum both on functions and on forms.
No associations
LandOfFree
The Marked Length Spectrum Versus the Laplace Spectrum on Forms on Riemannian Nilmanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Marked Length Spectrum Versus the Laplace Spectrum on Forms on Riemannian Nilmanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Marked Length Spectrum Versus the Laplace Spectrum on Forms on Riemannian Nilmanifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-310964