Differential invariants of self-dual conformal structures

被引：3

作者：

Kruglikov, Boris ^{[1
]}

Schneider, Eivind ^{[1
]}

机构：

[1] Univ Tromso, NT Fac, Inst Math & Stat, N-9037 Tromso, Norway

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2017年 / 113卷

关键词：

Differential invariants; Invariant derivations; Self-duality; Conformal metric structure; Hilbert polynomial; Poincare function;

D O I：

10.1016/j.geomphys.2016.05.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the jet-order, and the corresponding Poincare function. We describe the field of rational differential invariants separating generic orbits of the diffeomorphism pseudogroup action, resolving the local recognition problem for self-dual conformal structures. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：176 / 187

页数：12

共 14 条

[1]

Alekseevskij D.V., 1991, ENCY MATH SCI, V28

[2]

Besse A. L., 2007, EINSTEIN MANIFOLDS

[3] ALGEBRAIC LIE ALGEBRAS [J].

CHEVALLEY, C .

ANNALS OF MATHEMATICS, 1947, 48 (01) :91-100

[4] ON ALGEBRAIC LIE ALGEBRAS [J].

CHEVALLEY, C ;

TUAN, HF .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1945, 31 (07) :195-196

[5] On the Einstein-Weyl and conformal self-duality equations [J].

Dunajski, M. ;

Ferapontov, E. V. ;

Kruglikov, B. .

JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (08)

[6]

Grossman D.A., 2000, Selecta Math. (N.S.), V6, P399

[7]

Krasilshchik I.S., 1986, Advanced Studies in Contemporary Mathematics

[8] Differential Invariants and Symmetry: Riemannian Metrics and Beyond [J].

Kruglikov, B. .

LOBACHEVSKII JOURNAL OF MATHEMATICS, 2015, 36 (03) :292-297

[9]

Kruglikov B., 2016, J GEOM PHYS

[10]

Kruglikov B, 2008, HANDBOOK OF GLOBAL ANALYSIS, P725, DOI 10.1016/B978-044452833-9.50015-2

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