Tangent spaces and a metric on geodesic spaces (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In this work, we introduce a notion of tangent spaces to geodesic spaces with curvature bounded above. We first consider functions like inner products and angles with the functions. Further, we consider relations between newly proposed angle and the Alexandrov angle. We finally define the tangent space and a metirc on geodesic spaces.