On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds

GALAEV, Anton. On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds. Classical and Quantum Gravity. BRISTOL: Institute of Physics, 2014, vol. 31, No 13, 13 pp. ISSN 0264-9381. Available from: https://dx.doi.org/10.1088/0264-9381/31/13/135007.

Basic information

Original name

On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds

Authors

GALAEV, Anton

Edition

Classical and Quantum Gravity, BRISTOL, Institute of Physics, 2014, 0264-9381

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Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 3.168

DOI

http://dx.doi.org/10.1088/0264-9381/31/13/135007

UT WoS

000338698500007

Keywords in English

Lorentzian manifold; holonomy group; de Rham decomposition; Wu decomposition

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Abstract

V originále

It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold.