# Rigidity of isometric immersions into the light cone

## TL;DR

This paper proves the rigidity of isometric immersions of (n-1)-dimensional Riemannian manifolds into the light cone of Minkowski, de Sitter, and anti-de Sitter spacetimes for dimensions n≥3, highlighting geometric constraints.

## Contribution

It establishes the rigidity results for isometric immersions into light cones in various Lorentzian spacetimes, extending previous understanding of such geometric embeddings.

## Key findings

- Rigidity of isometric immersions into light cones proven for Minkowski, de Sitter, anti-de Sitter spacetimes.
- Results hold for dimensions n≥3.
- Provides new geometric constraints for embeddings into Lorentzian manifolds.

## Abstract

In this paper, we show the rigidity of isometric immersions for a Riemannian manifold of dimension $n-1$ into the light cone of $n+1$ dimensional Minkowski, de Sitter and anti-de Sitter spacetimes for $n\geq 3$.