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Differential fields and Geodesic flows II: Geodesic flows of pseudo-Riemannian algebraic varieties

  • Rémi JaouiEmail author
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Abstract

We define the notion of a smooth pseudo-Riemannian algebraic variety (X, g) over a field k of characteristic 0, which is an algebraic analogue of the notion of Riemannian manifold and we study, from a model-theoretic perspective, the algebraic differential equation describing the geodesics on (X, g).

When k is the field of real numbers, we prove that if the real points of X are Zariski-dense in X and if the real analytification of (X, g) is a compact Riemannian manifold with negative curvature, then the algebraic differential equation describing the geodesics on (X, g) is absolutely irreducible and its generic type is orthogonal to the constants.

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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Paris-SudOrsayFrance

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