Note on the Holonomy Groups of Pseudo-Riemannian Manifolds

GALAEV, Anton. Note on the Holonomy Groups of Pseudo-Riemannian Manifolds. Mathematical Notes. 2013, vol. 93, 5-6, p. 810--815. ISSN 0001-4346. Available from: https://dx.doi.org/10.1134/S0001434613050209.

Basic information

• Original name: Note on the Holonomy Groups of Pseudo-Riemannian Manifolds
• Authors: GALAEV, Anton (643 Russian Federation, guarantor, belonging to the institution).
• Edition: Mathematical Notes, 2013, 0001-4346.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Germany
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.259
• RIV identification code: RIV/00216224:14310/13:00068547
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1134/S0001434613050209
• UT WoS: 000321274300020
• Keywords in English: holonomy algebra; pseudo-Riemannian manifolds; linear connection; Levi-Civita connection; curvature tensor; Lorentzian manifold
• Tags: AKR, rivok, ZR

Abstract

For an arbitrary subalgebra h \subset so(r, s) a polynomial pseudo-Riemannian metric of signature (r + 2, s + 2) is constructed, the holonomy algebra of this metric contains h as a subalgebra. This result shows the essential distinction between the holonomy algebras of pseudoRiemannian manifolds of index greater than or equal to 2 and the holonomy algebras of Riemannian and Lorentzian manifolds.

Links

• EE2.3.20.0003, research and development project: Name: Algebraické metody v geometrii s potenciálem k aplikacím