Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one

2009 ◽  
Vol 79 (1) ◽  
pp. 1-10
Author(s):  
G. Calvaruso
Keyword(s):  
Three Dimensional ◽  
Lorentzian Metrics ◽  
Curvature Homogeneity

Certain homogeneous paracontact three-dimensional Lorentzian metrics

2017 ◽  
Vol 11 (01) ◽  
pp. 1850006
Author(s):  
Ali Haji-Badali ◽  
Elham Sourchi
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Einstein Manifolds ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lorentzian Metrics

In this paper, we study three-dimensional homogeneous paracontact metric manifolds for which the Reeb vector field of the underlying paracontact structure satisfies a nullity condition. We give example of paraSasakian and non-paraSasakian [Formula: see text]-manifolds. Finally, we exhibit explicit example of [Formula: see text]-Einstein manifolds.

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.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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