Article citationsMore>>

Petersen, P. (2006) Riemannian Geometry. 2nd Edition. Springer.

has been cited by the following article:

• TITLE: On the Curvature and Injectivity Radius Growth and Topology of Null Hypersurfaces in Lorentzian Manifolds

  AUTHORS: Ménédore Karimumuryango, Domitien Ndayirukiye, Nibaruta Gilbert

  KEYWORDS: Injectivity Radius, Rigging, Topology, Lorentzian Manifold, Lightlike Hypersurface

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.9, September 26, 2025

  ABSTRACT: We consider an associated Riemannian metric induced by a rigging defined on a neighborhood of the null hypersurface in a Lorentzian manifold, and we connect this null geometry with the associated Riemannian geometry. Using a rigging defined on some open set containing the lightlike hypersurface, we introduce a global geometric invariant Ra d ζ ( M ) related to injectivity radius to a closed complete noncompact null hypersurface in a Lorentzian manifold. Using some comparison theorems from non-degenerated geometry, we give the relationship between geometry and topology of a closed complete noncompact null hypersurface with associated Riemannian metric and the asymptotic properties of injectivity radiuses at infinity.