Girard Type Theorems for de Sitter Triangles with non-null Edges

TL;DR

This paper extends Girard's Theorem to proper de Sitter triangles with non-null edges, relating their area to interior angles in a new geometric context.

Contribution

It introduces Girard-type theorems for de Sitter triangles, providing a novel geometric relationship analogous to the spherical case.

Findings

Derived area-angle relationships for de Sitter triangles

Established analogues of Girard's Theorem in Lorentzian geometry

Extended classical spherical results to de Sitter space

Abstract

Girard's Theorem subjects to the area depending interior angles of a spherical triangle. In this paper, we introduce to its analogues for proper de Sitter triangles with non-null edges.