Key developments in geometry in the 19th Century

TL;DR

This paper reviews major 19th-century discoveries in geometry, such as intrinsic differential geometry and Riemannian geometry, which laid the groundwork for modern manifold theory in the 20th century.

Contribution

It highlights the historical development of geometric concepts that significantly influenced the evolution of modern geometry.

Findings

Development of intrinsic differential geometry

Introduction of projective geometry

Advancements in higher dimensional and Riemannian geometry

Abstract

This paper describes several key discoveries in the 19th century that led to the modern theory of manifolds in the twentieth century: intrinsic differential geometry, projective geometry and higher dimensional manifolds and Riemannian geometry.