On closed geodesics of lens spaces

On the diameter of some riemannian manifolds

We give a metric characterization of the Euclidean sphere in terms of the lower bound of the sectional curvature and the length of the shortest closed geodesics

The length of the shortest closed geodesics on a positively curved manifold

/pdf/rigidity-theorems-on-spheres-and-complex-projective-spaces-3gri110vpm.pdf

Rigidity Theorems on Spheres and Complex Projective Spaces

A general approach to proving that the length spectrum of a compact Riemannian manifold is an invariant of the Laplace spectrum comes from considering the wave trace, a spectrally determined tempered distribution. The Poisson relation states that the singularities of the wave trace can only occur at lengths of closed geodesics. Proving that the Poisson relation is an equality; i.e., every length of a closed geodesic is a singularity of the wave trace, yields an effective means of recovering the length spectrum from the Laplace spectrum. Regarding spaces of constant curvature this is known to be true for spaces of constant negative curvature. Continuing the study of space forms, we show that the Poisson relation is an equality for all flat manifolds, homogeneous lens spaces and three-dimensional lens spaces with fundamental group of prime order.

On the Poisson relation for flat and spherical space forms

https://projecteuclid.org/download/pdf_1/euclid.tmj/1178242590

This sixth edition illustrates the high degree of interplay between group theory and geometry The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups

On closed geodesics of lens spaces

Citations

On the diameter of some riemannian manifolds

The length of the shortest closed geodesics on a positively curved manifold

Rigidity Theorems on Spheres and Complex Projective Spaces

On the Poisson relation for flat and spherical space forms

References

Spaces of Constant Curvature

Related Papers (5)

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Closed geodesics on homogeneous spaces

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