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## 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

## SOME HOMOGENIZATION PROBLEMS

*Andrea Braides*

### in Gamma-Convergence for Beginners

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0004
- Subject:
- Mathematics, Applied Mathematics

Homogenization problems for a general class of integrals are solved by a direct approach. Different homogenization formulas are given, both in an asymptotic form and as a cell problem (in the convex ... More

## Introduction

*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/9780691153131.003.0001
- Subject:
- Mathematics, Geometry / Topology

This introductory chapter begins with a brief definition of conformal geometry. Conformal geometry is the study of spaces in which one knows how to measure infinitesimal angles but not lengths. A ... More

## Metrics on vector bundles

*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/9780199605880.003.0007
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

This chapter discusses the following: metrics and transition functions for real vector bundles; metrics and transition functions for complex vector bundles; metrics, algebra and maps; and a metric on ... More

## The Decomposition of Global Conformal Invariants (AM-182)

*Spyros Alexakis*

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153476
- eISBN:
- 9781400842728
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153476.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More

## Geodesics

*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/9780199605880.003.0008
- Subject:
- Mathematics, Geometry / Topology, Mathematical Physics

Let M denote a smooth manifold. A metric on TM can be used to define a notion of the distance between any two points in M and the distance travelled along any given path in M. This chapter first ... More

## Riemann Surfaces, Coverings, and Hypergeometric Functions

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More

## Conformai Curvature Tensors

*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/9780691153131.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form ... More

## Integration on a Compact Connected Lie Group

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0013
- Subject:
- Mathematics, Educational Mathematics

This chapter explores integration on a compact connected Lie group. One of the great advantages of working with a compact Lie group is the possibility of extending the notion of averaging from a ... More

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