Celebratio Mathematica — Singer — Complete Bibliography

Complete Bibliography

Works connected to Warren Arthur Ambrose

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W. Ambrose and I. M. Singer: “A theorem on holonomy,” Trans. Amer. Math. Soc. 75 : 3 (1953), pp. 428–443. MR 63739 Zbl 0052.18002 article

The object of this paper is to prove Theorem 2 of §2, which shows, for any connexion, how the curvature form generates the holonomy group. We believe this is an extension of a theorem stated without proof by E. Cartan [1926, p.4]. This theorem was proved after we had been informed of an unpublished related theorem of Chevalley and Koszul. We are indebted to S.-S. Chern for many discussions of matters considered here.

In §1 we give an exposition of some needed facts about connexions; this exposition is derived largely from an exposition of Chern [1951] and partly from expositions of H. Cartan [1951] and Ehresmann [1951]. We believe this exposition does however contain one new element, namely Lemma 1 of §1 and its use in passing from H. Cartan’s definition of a connexion (the definition given in §1) to E. Cartan’s structural equation.

W. Ambrose and I. M. Singer: “On homogeneous Riemannian manifolds,” Duke Math. J. 25 : 4 (1958), pp. 647–669. MR 102842 Zbl 0134.17802 article

W. Ambrose, R. S. Palais, and I. M. Singer: “Sprays,” An. Acad. Brasil. Ci. 32 : 2 (June 1960), pp. 163–178. MR 126234 Zbl 0097.37904 article

Richard Sheldon Palais	Related	Volume
Warren Arthur Ambrose	Related

I. M. Singer and H. Wu: “A tribute to Warren Ambrose,” Notices Amer. Math. Soc. 43 : 4 (April 1996), pp. 425–427. MR 1379775 Zbl 1044.01546 article

Hung-hsi Wu	Related
Warren Arthur Ambrose	Related