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Harmonic morphisms with one-dimensional fibres

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0012
Subject:
Mathematics, Pure Mathematics

This chapter shows that a harmonic morphism from a manifold of dimension n+1 to a manifold of dimension n is, locally or globally, a principal bundle with a certain metric. When n = 3, in a ... More


Harmonic morphisms from compact 3-manifolds

Paul Baird and John C. Wood

in Harmonic Morphisms Between Riemannian Manifolds

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.003.0010
Subject:
Mathematics, Pure Mathematics

This chapter shows that a non-constant harmonic morphism with compact fibres from a 3-manifold endows it with the structure of a Seifert fibre space — a 3-manifold with a certain type of ... More


Quadratic Surplus

Alfred Galichon

in Optimal Transport Methods in Economics

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691172767
eISBN:
9781400883592
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691172767.003.0006
Subject:
Economics and Finance, Microeconomics

This chapter considers the case when the attributes are d-dimensional vectors and the surplus is the scalar product; it assumes that the distribution of the workers' attributes is continuous, but it ... More


Hard Scattering Formalism

John Campbell, Joey Huston, and Frank Krauss

in The Black Book of Quantum Chromodynamics: A Primer for the LHC Era

Published in print:
2017
Published Online:
March 2018
ISBN:
9780199652747
eISBN:
9780191749148
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199652747.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The hard scattering formalism is introduced, starting from a physical picture based on the idea of equivalent quanta borrowed from QED, and the notion of characteristic times. Contact to the standard ... More


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