Curvature and Symmetries of Parallel Transport

摘要

Based on our human sensations and perceptions of "the physical geometry of what we experience as being our ambient world", and, after a long history as an experimental science in various cultures around the globe, finally geometry was established as the central field of mathematics in the world of the Old Greeks. And still today, as such formulated by Chern in his introduction to [53]: "While algebra and analysis provide the foundations of mathematics, geometry is at the core". From Serres' "Les origines de la geometric" , in this respect we freely quote the following: "Ainsi l'elimination de ce qui cache la forme, ainsi l'exclusion de tout sujet, rendent possible une science pour l'Universel pour nous et, en rigueur et en verite, dans l'Universel en soi. Les mathematiques vinrent d'identifier l'un a l'autre." Thus being conceived in the human mind via psychologically created von Helmholtz-hypotheses about "our surrounding world and its contents", which were and are made at service to the evolution of our species and its individuals, abstract geometry was born and has grown ever since by brain-design.