Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson-Walker spacetimes

Luis J. Alias; Josue Melendez; Matias Navarro; Didier A. Solis

Home/Archive/arXiv

arXiv · 2508.13852

Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson-Walker spacetimes

Luis J. Alias·Josue Melendez·Matias Navarro·Didier A. Solis

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study codimension two spacelike submanifolds contained into a general class of null hypersurfaces in generalized Robertson-Walker spacetimes, refer to as nullcones. In particular we analyze light cones and lightlike cylinders in Lorentz-Minkowski spacetime, as well as null cones in de Sitter spacetime. We give conditions on a radial coordinate that guarantee that such a spacelike submanifold is conformally diffeomorphic to the hyperbolic space, a round cylinder a sphere; respectively. We also provide some non-existence results for weakly trapped submanifolds.

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Luis J. Alias, Josue Melendez, Matias Navarro, Didier A. Solis. 2025-08-19. Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson-Walker spacetimes. https://arxiv.org/abs/2508.13852

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Futaki invariant on Hopf manifolds

The Futaki invariant is a fundamental tool in Kähler geometry representing an obstruction to the existence of Kähler-Einstein metrics. Recently, it was generalized to compact complex manifolds. In this paper, we prove that it vanishes on Hopf manifolds.

math.DG↗

arXiv2026

Remarks on potential functions of noncompact quasi-Einstein manifolds

In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat.

math.DG↗

arXiv2026

Adjusted connections on non-abelian bundle gerbes

Higher gauge theory for non-abelian structure 2-groups faces significant challenges when extending beyond the fake-flat sector, which suffers from limited applicability in physical models. A promising resolution involves equipping 2-groups with additional structure, known as adjustments. We present a comprehensive theory of adjusted connections on non-abelian bundle gerbes, classified by Saemann's adjusted version of non-abelian differential cohomology. This theory enables, in particular, a new coordinate-independent formulation of Tellez-Dominguez' lifting theorem, establishing a correspondence between adjusted connections on non-abelian bundle gerbes and connections on abelian bundle 2-gerbes.

math.DG↗