The half-space model of pseudo-hyperbolic space

Andrea Seppi (1) , Enrico Trebeschi (2)

1 IF - Institut Fourier
2 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]

In this note we develop a half-space model for the pseudo-hyperbolic space $\mathbb{H}^{p,q}$, for any $p,q$ with $p\geq 1$. This half-space model embeds isometrically onto the complement of a degenerate totally geodesic hyperplane in $\mathbb{H}^{p,q}$. We describe the geodesics, the totally geodesic submanifolds, the horospheres, the isometry group in the half-space model, and we explain how to interpret the boundary at infinity in this setting.

Domaines: Géométrie différentielle [math.DG]

Andrea Seppi, Enrico Trebeschi. The half-space model of pseudo-hyperbolic space. X International Meeting on Lorentzian Geometry, Jun 2020, Granada, Spain. ⟨hal-03421097v1⟩