Four-dimensional Einstein-like manifolds and curvature homogeneity

1995 ◽  
Vol 54 (3) ◽  
pp. 225-243 ◽  
Author(s):  
Fabio Podest� ◽  
Andrea Spiro
Keyword(s):  
Curvature Homogeneity

A common generalization of curvature homogeneity theories

2020 ◽  
Vol 111 (1) ◽  
Author(s):  
Corey Dunn ◽  
Alexandro Luna ◽  
Sammy Sbiti
Keyword(s):  
Common Generalization ◽  
Curvature Homogeneity

Singer invariants and various types of curvature homogeneity

2013 ◽  
Vol 45 (4) ◽  
pp. 303-317 ◽  
Author(s):  
Corey Dunn ◽  
Cullen McDonald
Keyword(s):  
Curvature Homogeneity

scholarly journals THE CURVATURE HOMOGENEITY BOUND FOR LORENTZIAN FOUR-MANIFOLDS

2009 ◽  
Vol 06 (01) ◽  
pp. 99-127 ◽  
Author(s):  
R. MILSON ◽  
N. PELAVAS
Keyword(s):  
Electromagnetic Radiation ◽  
Lorentzian Manifold ◽  
De Sitter ◽  
Curvature Homogeneity ◽  
Seventh Order ◽  
Sitter Background ◽  
Four Manifolds ◽  
Locally Homogeneous ◽  
Radiation Type

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2manifolds that are not homogeneous. The resulting metrics belong to the class of null electromagnetic radiation, type N solutions on an anti-de Sitter background. These findings prove that the four-dimensional Lorentzian Singer number k1,3= 3, falsifying some recent conjectures [1]. We also prove that invariant classification for these proper CH2solutions requires ∇(7)R, and that these are the unique metrics requiring the seventh order.

scholarly journals Curvature homogeneity of affine connections on two-dimensional manifolds

1999 ◽  
Vol 81 (1) ◽  
pp. 123-139 ◽  
Author(s):  
Oldřich Kowalski ◽  
Barbara Opozda ◽  
Zdeněk Vlášek
Keyword(s):  
Two Dimensional ◽  
Affine Connections ◽  
Curvature Homogeneity

scholarly journals Homothety curvature homogeneity and homothety homogeneity

2015 ◽  
Vol 48 (2) ◽  
pp. 149-170 ◽  
Author(s):  
E. García-Río ◽  
P. Gilkey ◽  
S. Nikčević
Keyword(s):  
Curvature Homogeneity

Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One

2010 ◽  
Vol 53 (3) ◽  
pp. 412-424 ◽  
Author(s):  
G. Calvaruso
Keyword(s):  
Three Dimensional ◽  
Null Line ◽  
Line Field ◽  
Lorentz Manifolds ◽  
Curvature Homogeneity ◽  
Lorentz Metrics

AbstractWe completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.

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