Midpoint Characterization in Symmetric Hadamard Spaces and its Applications

Subject Areas : Mathematical Analysis

Farshid Khojasteh ¹

1 - Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran.

Received: 2022-03-04 Accepted : 2022-02-11 Published : 2022-05-01

Keywords: Hadamard space, Quasi linearization, CAT(0) spaces, Midpoint, Affine maps,

Abstract :

In this paper, we characterize symmetric Hadamard spaces by the help of new midpoint propertiesin these spaces and show that any symmetric Hadamard spaces are flat. As an application of the newmidpoint property we characterize the affine mapping in these spaces.