Projective collineations as products of homologies, elations, and projective reflections

1982 ◽  
Vol 25 (1) ◽  
pp. 116-117
Author(s):  
Erich W. Ellers
Keyword(s):  
Projective Collineations

scholarly journals Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1018
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Differential Equations ◽  
Riemannian Space ◽  
Dimensional Subspace ◽  
Geometric Construction ◽  
Lie Point Symmetries ◽  
Geodesic Equations ◽  
Symmetries Of Differential Equations ◽  
Projective Collineations

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study, we prove that the projective collineations of a n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

PROPER PROJECTIVE SYMMETRY IN THE SCHWARZSCHILD METRIC

2006 ◽  
Vol 21 (23) ◽  
pp. 1795-1802 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Schwarzschild Metric ◽  
Integration Techniques ◽  
Projective Collineations

A study of proper projective symmetry in the Schwarzschild metric is given by using algebric and direct integration techniques. It is shown that projective collineations admitted by the above metric are the Killing vector fields.

Projective collineations as products of homologies, elations, and projective reflections

1982 ◽  
Vol 25 (1) ◽  
pp. 103-114 ◽  
Author(s):  
Erich W. Ellers
Keyword(s):  
Projective Collineations

scholarly journals Lie symmetries of geodesic equations and projective collineations

2010 ◽  
Vol 62 (1-2) ◽  
pp. 203-214 ◽  
Author(s):  
Michael Tsamparlis ◽  
Andronikos Paliathanasis
Keyword(s):  
Lie Symmetries ◽  
Geodesic Equations ◽  
Projective Collineations

scholarly journals Lie symmetries of the geodesic equations and projective collineations

2009 ◽  
Vol 189 ◽  
pp. 012042
Author(s):  
Michael Tsamparlis ◽  
Andronikos Paliathanasis
Keyword(s):  
Lie Symmetries ◽  
Geodesic Equations ◽  
Projective Collineations

PROJECTIVE COLLINEATIONS AS PRODUCTS OF CYCLIC COLLINEATIONS

1979 ◽  
Vol 12 (4) ◽  
Author(s):  
Krzysztof Witczyúski
Keyword(s):  
Projective Collineations

Projective collineations in spacetimes

1995 ◽  
Vol 12 (4) ◽  
pp. 1007-1020 ◽  
Author(s):  
G S Hall ◽  
D P Lonie
Keyword(s):  
Projective Collineations

PROPER PROJECTIVE SYMMETRY IN KANTOWSKI–SACHS AND BIANCHI TYPE III SPACETIMES

2007 ◽  
Vol 22 (29) ◽  
pp. 2209-2216 ◽  
Author(s):  
GHULAM SHABBIR ◽  
AMJAD ALI
Keyword(s):  
Bianchi Type ◽  
Direct Integration ◽  
Type Iii ◽  
Integration Techniques ◽  
Projective Collineations

A study of Kantowski–Sachs and Bianchi type III spacetimes according to their proper projective symmetry is given by using the algebraic and direct integration techniques. It is shown that the above spacetimes do not admit proper projective collineations.

Projective collineations in Einstein spaces

1993 ◽  
Vol 10 (6) ◽  
pp. 1139-1145 ◽  
Author(s):  
A Barnes
Keyword(s):  
Einstein Spaces ◽  
Projective Collineations

A note on projective collineations

1972 ◽  
Vol 23 (1) ◽  
pp. 446-448
Author(s):  
Frederick W. Stevenson
Keyword(s):  
Projective Collineations
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