Holonomy groups of Lorentzian manifolds: classification, examples, and applications

Recent Developments in Pseudo-Riemannian Geometry ◽

10.4171/051-1/2 ◽

2009 ◽

pp. 53-96 ◽

Cited By ~ 17

Author(s):

Anton Galaev ◽

Thomas Leistner

Keyword(s):

Lorentzian Manifolds ◽

Holonomy Groups

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Holonomy Groups of Lorentzian Manifolds: A Status Report

Global Differential Geometry - Springer Proceedings in Mathematics ◽

10.1007/978-3-642-22842-1_7 ◽

2011 ◽

pp. 163-200 ◽

Cited By ~ 8

Author(s):

Helga Baum

Keyword(s):

Status Report ◽

Lorentzian Manifolds ◽

Holonomy Groups

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Holonomy groups of Lorentzian manifolds

Russian Mathematical Surveys ◽

10.1070/rm2015v070n02abeh004947 ◽

2015 ◽

Vol 70 (2) ◽

pp. 249-298 ◽

Cited By ~ 4

Author(s):

A S Galaev

Keyword(s):

Lorentzian Manifolds ◽

Holonomy Groups

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Conformally flat Lorentzian manifolds with special holonomy groups

Sbornik Mathematics ◽

10.1070/sm2013v204n09abeh004339 ◽

2013 ◽

Vol 204 (9) ◽

pp. 1264-1284 ◽

Cited By ~ 1

Author(s):

A S Galaev

Keyword(s):

Conformally Flat ◽

Lorentzian Manifolds ◽

Special Holonomy ◽

Holonomy Groups

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Four-dimensional homogeneous Lorentzian manifolds

Monatshefte für Mathematik ◽

10.1007/s00605-013-0588-9 ◽

2013 ◽

Vol 174 (3) ◽

pp. 377-402 ◽

Cited By ~ 7

Author(s):

Giovanni Calvaruso ◽

Amirhesam Zaeim

Keyword(s):

Lorentzian Manifolds

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On the Length of Loops Generating Holonomy Groups

Bulletin of the London Mathematical Society ◽

10.1112/blms/23.4.372 ◽

1991 ◽

Vol 23 (4) ◽

pp. 372-374 ◽

Cited By ~ 1

Author(s):

D. R. Wilkins

Keyword(s):

Holonomy Groups

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Holonomy groups of Riemann spaces

Ukrainian Mathematical Journal ◽

10.1007/bf01086833 ◽

1968 ◽

Vol 19 (2) ◽

pp. 212-215

Author(s):

D. V. Alekseevskii

Keyword(s):

Holonomy Groups

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FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887806001739 ◽

2006 ◽

Vol 03 (07) ◽

pp. 1349-1357 ◽

Cited By ~ 17

Author(s):

V. V. KOZLOV ◽

I. V. VOLOVICH

Keyword(s):

Mass Spectrum ◽

Elliptic Equations ◽

Gordon Equation ◽

Infinite Family ◽

De Sitter ◽

Lorentzian Manifolds ◽

Klein Gordon ◽

Finite Action ◽

Discrete Mass ◽

Klein Gordon Equation

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

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