Appendix A . Jacobi Fields And Toponogov'S Theorem For Lorentzian Manifolds

2017 ◽  
pp. 567-572
Keyword(s):  
Lorentzian Manifolds ◽  
Jacobi Fields ◽  
Toponogov’S Theorem

Four-dimensional homogeneous Lorentzian manifolds

2013 ◽  
Vol 174 (3) ◽  
pp. 377-402 ◽  
Author(s):  
Giovanni Calvaruso ◽  
Amirhesam Zaeim
Keyword(s):  
Lorentzian Manifolds

scholarly journals FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

2006 ◽  
Vol 03 (07) ◽  
pp. 1349-1357 ◽  
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.

A Toponogov splitting theorem for Lorentzian manifolds

1985 ◽  
pp. 1-13 ◽  
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich ◽  
Steen Markvorsen ◽  
Gregory J. Galloway
Keyword(s):  
Splitting Theorem ◽  
Lorentzian Manifolds

scholarly journals On the Study of Jacobi Fields in Riemannian Manifolds

1970 ◽  
Vol 43 (4) ◽  
pp. 521-528
Author(s):  
Khondokar M Ahmed
Keyword(s):  
Field Equation ◽  
Key Words ◽  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Jacobi Equation ◽  
Standard Form ◽  
Jacobi Field ◽  
Jacobi Fields ◽  
New Approach

A new approach of finding a Jacobi field equation with the relation between curvature and geodesics of a Riemanian manifold M has been derived. Using this derivation we have made an attempt to find a standard form of this equation involving sectional curvature K and other related objects. Key words: Riemanign curvature, Sectional curvature, Jacobi equation, Jacobifield.    doi: 10.3329/bjsir.v43i4.2242 Bangladesh J. Sci. Ind. Res. 43(4), 521-528, 2008

Jacobi Fields, Conjugate Points

2020 ◽  
pp. 45-57
Author(s):  
Walter Dittrich ◽  
Martin Reuter
Keyword(s):  
Conjugate Points ◽  
Jacobi Fields
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