Spaces of geodesics of pseudo-Riemannian space forms and normal congruences of hypersurfaces
Year: 2013
Type: article
Abstract: We describe natural Kähler or para-Kähler structures of the spaces of geodesics of pseudo-Riemannian space forms and relate the local geometry of hypersurfaces of space forms to that of their normal congruences, or Gauss maps, which are Lagrangian submanifolds. The space of geodesics L ± ( S p , 1 n + 1 ) L^{\pm }(\mathbb {S}^{n+1}_{p,1}) of a pseudo-Riemannian space form S p , 1 n + 1 \mathbb {S}^{n+1}_{p,1} of non-vanishing curvature enjoys a Kähler or para-Kähler structure ( J , G ) (\mathbb {J},\mathbb {G}) which is in addition Einstein. Moreover, in the three-dimensional case, L ± ( S p , 1 n + 1 ) L^{\pm }(\mathbb {S}^{n+1}_{p,1}) enjoys another Kähler or para-Kähler structure ( J ′ , G ′ ) (\mathbb {J}’,\mathbb {G}’) which is scalar flat. The normal congruence of a hypersurface S \mathcal {S} of S p , 1 n + 1
Author: Henri Anciaux
Institution: Universidade de São Paulo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2083819982