2017/11/25 by S. G. Elgendi, Elgendi, S. G.
Mathematics · Physics and Astronomy · #49N45 #53B40 #53C60 #58B20 #58E30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1711.09204
openalex publication_date 2017/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the notion of one form deformation of sprays. The metrizability of the new spray, when the background spray is flat, is characterized. Therefore, we obtain new projectively flat metrics of constant flag curvature 1. Moreover, these new metrics are not, generally, isometric to the Klein metric via affine transformations. New solutions for Hilbert's fourth problem are obtained and constructed. Various examples are discussed and studied.