Metrisability of three-dimensional path geometries

被引：13

作者：

Dunajski, Maciej ^{[1
]}

Eastwood, Michael ^{[2
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England

[2] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2016年 / 2卷 / 03期

关键词：

Projective differential geometry; Path geometry; Weyl geometry; Metrisability;

D O I：

10.1007/s40879-016-0095-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant tensors algebraically constructed from the projective Weyl curvature. We show, by examples, that their vanishing is necessary but not sufficient for local metrisability.

引用

页码：809 / 834

页数：26

共 23 条

[1] Baston R. J., 1989, PENROSE TRANSFORM
[2] Bryant R, 2009, J DIFFER GEOM, V83, P465
[3] CAP A, 2009, MATH SURVEYS MONOGRA, V0154
[4] Casey S., 2013, THESIS U CAMBRIDGE
[5] CLIFFORD WK, 1881, MATH FRAGMENTS BEING
[6] Eastwood M, 2008, IMA VOL MATH APPL, V144, P339
[7] Egorov I. P., 1951, DOKL AKAD NAUK SSSR, V80, P709
[8] Degree of mobility for metrics of Lorentzian signature and parallel (0,2)-tensor fields on cone manifolds
Fedorova, Aleksandra
Matveev, Vladimir S.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 108 : 1277 - 1312
[9] FELS ME, 1995, P LOND MATH SOC, V71, P221
[10] Fulton W., 1991, REPRESENTATION THEOR

← 1 2 3 →