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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


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


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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