Jump to ContentJump to Main Navigation

You are looking at 1-12 of 12 items

  • Keywords: Riemannian geometry x
Clear All Modify Search

View:

The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

Claude LeBrun

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/9780199534920.003.0003
Subject:
Mathematics, Geometry / Topology

Nigel Hitchin has played a key role in the exploration of four-dimensional Riemannian geometry, and in particular has made foundational contributions to the theory of self-dual manifolds, ... More


Gravitation

Reinhold A. Bertlmann

in Anomalies in Quantum Field Theory

Published in print:
2000
Published Online:
February 2010
ISBN:
9780198507628
eISBN:
9780191706400
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507628.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on gravitation. It first reviews some basic concepts of the Riemannian geometry and establishes notation. It then discusses the gravitational action, specifically the fermionic ... More


Riemannian Geometry

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The key notions of the differential and Riemannian geometry necessary for understanding the General Relativity are introduced here. We provide the reader with the necessary tools for study the ... More


Relativity, Gravitation and Cosmology: A Basic Introduction

Ta-Pei Cheng

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199573639
eISBN:
9780191722448
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573639.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Einstein's general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, the principle of equivalence, Riemannian ... More


Geometry

Olivier Darrigol

in Physics and Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present

Published in print:
2014
Published Online:
June 2014
ISBN:
9780198712886
eISBN:
9780191781360
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198712886.003.0004
Subject:
Physics, History of Physics

This chapter deals with the foundations of geometry, with emphasis on Helmholtz’s approach to this problem in the late 1860s. It is first recalled how the ancient belief in the apodictic truth of the ... More


Geodesics

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

Riemannian geometry deals with distances of infinitesimally close points. A curve of minimal length is a geodesic. This variational principle happens to have the same structure as that of mechanics, ... More


Riemann Surfaces

Simon Donaldson

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198526391
eISBN:
9780191774874
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526391.001.0001
Subject:
Mathematics, Geometry / Topology, Analysis

The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an ... More


Curvature and Instability

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0011
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

The Euler equations of a rigid body can be understood as the geodesic equations for a metric on the rotation group. A rapid introduction to the Riemannian geometry of Lie groups (following Milnor) is ... More


Towards a general theory of relativity

Ta-Pei Cheng

in Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199669912
eISBN:
9780191744488
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669912.003.0012
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

In general relativity (GR) physics laws are not changed under general coordinate transformations. Among Einstein’s motivation for GR was his wish to have a deeper understanding of the empirically ... More


Jet Isomorphism

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/9780691153131.003.0008
Subject:
Mathematics, Geometry / Topology

A fundamental result in Riemannian geometry is the jet isomorphism theorem which asserts that at the origin in geodesic normal coordinates, the full Taylor expansion of the metric may be recovered ... More


General Relativity as a Geometric Theory of Gravity

Ta-Pei Cheng

in A College Course on Relativity and Cosmology

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199693405
eISBN:
9780191803130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199693405.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The mathematics of a curved manifold is Riemannian geometry. This chapter first presents some basic elements of Gaussian coordinates and the metric tensor. From the requirement that a curve have the ... More


Basic notions

Piotr T. Chruściel

in Geometry of Black Holes

Published in print:
2020
Published Online:
December 2020
ISBN:
9780198855415
eISBN:
9780191889233
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198855415.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to set the ground for the remainder of this work. We present our conventions and notations in Section 1.1. We review some basic facts about the topology of manifolds in ... More


View: