Geodesic Conjugacy in two-step nilmanifolds

1995/03/15 by Gordon, Carolyn, Mao, Yiping
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9503220

Abstract

Two Riemannian manifolds are said to have C^k-conjugate geodesic flows if there exist an C^k diffeomorphism between their unit tangent bundles which intertwines the geodesic flows. We obtain a number of rigidity results for the geodesic flows on compact 2-step Riemannian nilmanifolds: For generic 2-step nilmanifolds the geodesic flow is C² rigid. For special classes of 2-step nilmanifolds, we show that the geodesic flow is C⁰ or C² rigid. In particular, there exist continuous families of 2-step nilmanifolds whose Laplacians are isospectral but whose geodesic flows are not C⁰ conjugate.

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