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Flat and almost flat manifolds

Stanley Chang and Shmuel Weinberger

in Quantum Mechanics

Published in print:
2019
Published Online:
May 2021
ISBN:
9780691160498
eISBN:
9780691200354
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160498.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter investigates flat and almost flat manifolds. Flat manifolds have metrics whose Riemannian curvature is identically zero. By a theorem of Bieberbach, they are finitely covered by the ... More


Two papers which changed my life: Mil nor's seminal work on flat manifolds and bundles

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0024
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter surveys developments arising from John Milnor's 1958 paper, “On the existence of a connection with curvature zero” and his 1977 paper, “On fundamental groups of complete affinely flat ... More


Conformally Flat and Conformally Einstein Spaces

Charles Fefferman and C. Robin Graham

in The Ambient Metric (AM-178)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter analyzes the ambient and Poincaré metrics for locally conformally flat manifolds and for conformal classes containing an Einstein metric. The obstruction tensor vanishes for even ... More


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