Rigidity of causal maps

TL;DR

This paper proves that order-invariant injective maps on a specific noncompactly causal symmetric space are necessarily elements of a particular orthogonal group, revealing a rigidity property of these maps.

Contribution

It establishes a rigidity result for order-invariant injective maps on the noncompactly causal symmetric space $SO_0(1,n)/SO_0(1,n-1)$, showing they belong to $O(1,n)^+$.

Findings

Order-invariant injective maps are in $O(1,n)^+$.

The result applies to the noncompactly causal symmetric space.

It demonstrates a rigidity property of these maps.

Abstract

We show that order-invariant injective maps on the noncompactly causal symmetric space $SO_0 (1,n)/SO_0 (1,n-1)$ belong to $O(1,n)^+$.