Gaussian beams on Zoll manifolds and maximally degenerate Laplacians

Steve Zelditch

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arXiv · 1404.2906

Gaussian beams on Zoll manifolds and maximally degenerate Laplacians

Steve Zelditch

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Abstract

Gaussian beams exist along all closed geodesics of a Zoll surface, despite the fact that the algorithm for constructing them assumes that the closed geodesics are non-degenerate. Similarly, there exists a global Birkhoff normal for a Zoll Laplacian despite the degeneracy. We explain why both algorithms work in the Zoll case and give an exact formula for the sub-principal normal form invariant. In the case of "maximally degenerate" Zoll Laplacians, this invariant vanishes and we obtain new geometric constraints on such Zoll metrics.

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BibTeX RIS

Steve Zelditch. 2014-04-10. Gaussian beams on Zoll manifolds and maximally degenerate Laplacians. https://arxiv.org/abs/1404.2906

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