Homogeneous geodesics and natural reductivity of homogeneous Gödel-type spacetimes

2021 ◽  
Vol 159 ◽  
pp. 103919
Author(s):  
Giovanni Calvaruso ◽  
Amirhesam Zaeim
Keyword(s):  
Homogeneous Geodesics

scholarly journals Riemannian generalized C-spaces with homogeneous geodesics

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1117-1124
Author(s):  
Andreas Arvanitoyeorgos ◽  
Huajun Qin ◽  
Yu Wang ◽  
Guosong Zhao
Keyword(s):  
Necessary Conditions ◽  
Homogeneous Spaces ◽  
Invariant Metric ◽  
Homogeneous Geodesics

We investigate homogeneous geodesics in a class of homogeneous spaces G/K' called generalized C-spaces. We give necessary conditions so that a G-invariant metric on G/K' is a g.o. metric.

Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds

2015 ◽  
Vol 46 (1) ◽  
pp. 23-64 ◽  
Author(s):  
Giovanni Calvaruso ◽  
Anna Fino ◽  
Amirhesam Zaeim
Keyword(s):  
Homogeneous Geodesics

Homogeneous geodesics and the critical points of the restricted Finsler function

2011 ◽  
Vol 46 (1) ◽  
pp. 12-16 ◽  
Author(s):  
Parastoo Habibi ◽  
Dariush Latifi ◽  
Megerdich Toomanian
Keyword(s):  
Critical Points ◽  
Homogeneous Geodesics

scholarly journals Homogeneous geodesics in pseudo-Riemannian nilmanifolds

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Viviana del Barco
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Orbit Space ◽  
Nilpotent Lie Groups ◽  
Invariant Metric ◽  
Natural Parameter ◽  
Geodesic Orbit Space ◽  
Affine Parameter ◽  
Homogeneous Geodesics

AbstractWe study the geodesic orbit property for nilpotent Lie groups N endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on itself by left-translations we show that it is a geodesic orbit space if and only if the metric is bi-invariant. Assuming N is 2-step nilpotent and with non-degenerate center we give algebraic conditions on the Lie algebra n of N which imply that every geodesic is the orbit of a one-parameter subgroup of N.Auto(N). In addition we present an example of an almost g.o. space such that for null homogeneous geodesics, the natural parameter of the orbit is not always the affine parameter of the geodesic.

scholarly journals The Existence of Two Homogeneous Geodesics in Finsler Geometry

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 850
Author(s):  
Zdeněk Dušek
Keyword(s):  
Finsler Geometry ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Homogeneous Geodesics ◽  
Homogeneous Geodesic ◽  
Randers Metrics

The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.

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