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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

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

V originále

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