The Phase Space of k-Surfaces

François Labourie ()
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François Labourie: Université Paris-Sud, Topologie et Dynamique

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 295-307 from Springer

Abstract: Abstract The purpose of this note is to provide an introduction to several articles concerning k-surfaces [7], [6], and more specially random ones [8]. Recall briefly that a k-surface is an immersed surface in a Riemannian manifold with curvature less than -1, such that the product of the principal curvatures is k, where k ∈ ]0,1[. Following these articles, we explain that k-surfaces possess (like geodesics) a “genuine” laminated phase space which has chaotic properties similar to those of the geodesic flow, and that, furthermore, the dynamics on this space can be coded, hence producing transversal measures.

Keywords: Phase Space; Invariant Measure; Constant Curvature; Closed Geodesic; Full Support (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_15

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DOI: 10.1007/978-3-662-04743-9_15

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