23/03/27 12:02:51.50 ZryxA1Gf.net
>>190
ありがとう
tractorが、不勉強で初見だな
URLﾘﾝｸ(arxiv.org)
[Submitted on 23 Dec 2014 (v1), last revised 1 Aug 2015 (this version, v2)]
An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity
Sean Curry, A. Rod Gover
Abstract. The following are expanded lecture notes for the course of eight one
hour lectures given by the second author at the 2014 summer school Asymptotic
Analysis in General Relativity held in Grenoble by the Institut Fourier. The
first four lectures deal with conformal geometry and the conformal tractor calculus, taking as primary motivation the search for conformally invariant tensors
and diffrerential operators. The final four lectures apply the conformal tractor
calculus to the study of conformally compactified geometries, motivated by the
conformal treatment of infinity in general relativity.
Contents
0. Introduction 2
0.1. Notation and conventions 4
1. Lecture 1: Riemannian invariants and invariant operators 6
1.1. Ricci calculus and Weyl’s invariant theory 7
1.2. Invariant operators, and analysis 8
2. Lecture 2: Conformal transformations and conformal covariance 9
2.1. Conformal Transformations 9
P4
Also left out in these notes is any discussion of conformal spin geometry. In this
case there is again a canonical tractor calculus, known as spin tractor calculus or
local twistor calculus, which is a refinement of the usual conformal tractor calculus
in the same way that spinor calculus is a refinement of the usual tensor calculus
on pseudo-Riemannian spin manifolds. The interested reader is referred to [4, 50].