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Sasakian Geometry

Charles Boyer and Krzysztof Galicki

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.001.0001
Subject:
Mathematics, Geometry / Topology

Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an ... More


Harmonic Morphisms Between Riemannian Manifolds

Paul Baird and John C. Wood

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198503620
eISBN:
9780191708435
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198503620.001.0001
Subject:
Mathematics, Pure Mathematics

Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic ... More


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


Riemannian manifolds and conformality

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/9780198503620.003.0002
Subject:
Mathematics, Pure Mathematics

This chapter introduces fundamental concepts from Riemannian geometry, including the Laplacian and harmonic functions on a Riemannian manifold. The next two sections discuss weak conformality and the ... More


Fundamental properties of harmonic morphisms

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/9780198503620.003.0004
Subject:
Mathematics, Pure Mathematics

This chapter characterizes harmonic morphisms between Riemannian manifolds and discusses their basic properties. The first non-constant term of the Taylor series of a harmonic morphism at a point ... More


Entropy for hyperbolic Riemann surface laminations II

Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony

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/9780691159294.003.0021
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated ... More


Thurston's Proof

Benson Farb and Dan Margalit

in A Primer on Mapping Class Groups (PMS-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.003.0016
Subject:
Mathematics, Geometry / Topology

This chapter describes Thurston's original path of discovery to the Nielsen–Thurston classification theorem. It first provides an example that illustrates much of the general theory, focusing on ... More


Flat connections and holonomy

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0013
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines flat connections. A connection on a principal bundle is said to be flat when its curvature 2-form is identically zero. The discussions cover flat connections on bundles over the ... More


Entropy for hyperbolic Riemann surface laminations I

Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony

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/9780691159294.003.0020
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of ... More


Teichmuller Geometry

Benson Farb and Dan Margalit

in A Primer on Mapping Class Groups (PMS-49)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147949
eISBN:
9781400839049
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147949.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines ... More


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