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Foliations

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0003
Subject:
Mathematics, Geometry / Topology

As Sasakian manifolds are all examples of Riemannian foliations with one-dimensional leaves, this chapter goes into the world of foliations with a particular focus on the Riemannian case. Haeiger ... More


Structures on Manifolds

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter begins by introducing various geometries that play important roles in the way they relate to Sasakian structures. It espouses the point of view that a geometric structure is best ... More


Sasakian Structures, Killing Spinors, and Supersymmetry

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0015
Subject:
Mathematics, Geometry / Topology

This chapter gives a very brief overview of the rich theory of Killing spinors describing Bär's correspondence which connects Sasaki-Einstein geometry to Berger's holonomy theorem. It is then shown ... More


Non‐Embedding and Non‐Extension Results in Special Holonomy

Robert L. Bryant

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0017
Subject:
Mathematics, Geometry / Topology

In the early analyses of metrics with special holonomy in dimensions 7 and 8, particularly in regards to their existence and generality, heavy use was made of the Cartan–Kähler theorem, essentially ... More


Yang–Mills theories

Rodolfo Gambini and Jorge Pullin

in A First Course in Loop Quantum Gravity

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199590759
eISBN:
9780191774980
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199590759.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces Yang-Mills theories as a natural generalization of Maxwell's theory. It discusses covariant derivatives and the Yang-Mills equations, which it also considers in a Hamiltonian ... More


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