Surveys in Differential Geometry

Volume 26 (2021)

Revisiting S.S. Chern’s article “The geometry of $G$-structures”, 55 years after its publication

Pages: 1 – 11

DOI: https://dx.doi.org/10.4310/SDG.2021.v26.n1.a1

Author

Jean-Pierre Bourguignon (Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France)

Abstract

Professor Chern Shiing-Shen contributed to Geometry in many different ways, proving important results and, on many occasions, providing a view on how the field could move forward. One of his articles that both presented a remarkable synthesis of new developments and offered his vision for future ones is “The Geometry of $G$-structures,” published in 1966.

In the present text, I propose an analysis of the article’s main features. It also contains a testimony by Chern himself on how some of his main contributions came about and his view on what may come next, that proved remarkably correct.

Full Text (PDF format)

A lecture given at Tsinghua University, 11 October 2021 on the occasion of the celebration of Professor S.S. Chern’s 110th birthday

Published 22 January 2024