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- W2593397181 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." @default.
- W2593397181 created "2017-03-16" @default.
- W2593397181 creator A5072549541 @default.
- W2593397181 date "2017-03-01" @default.
- W2593397181 modified "2023-09-26" @default.
- W2593397181 title "Differential fields and Geodesic flows II : Geodesic flows of pseudo-Riemannian algebraic varieties" @default.
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