The Carnot Theorem in Einstein Gyrovector Spaces

Abstract

In Euclidean geometry, Carnot’s theorem is a direct application of the theorem Pythagoras. In [4,6] A.A. Ungar, employs the Einstein gyrovector spaces for the introduction of the gyrotrigonometry. Ungar’s and other researcher’s works play a major role in translating some theorems from Euclidean geometry to corresponding theorems in Einstein gyrovector spaces.In [2] Demirel and Soytürk proved that hyperbolic Carnot theorem. In this paper, we present Carnot’s theorem in Einstein’s gyrovector spaces in terms of gamma factors.