scholarly journals Conformal Killing Tensors and Variable Separation for Hamilton–Jacobi Equations

1983 ◽  
Vol 14 (1) ◽  
pp. 126-137 ◽  
Author(s):  
E. G. Kalnins ◽  
Willard Miller, Jr.
Keyword(s):  
Conformal Killing ◽  
Variable Separation ◽  
Killing Tensors ◽  
Jacobi Equations

scholarly journals Conformal geodesics on gravitational instantons

2021 ◽  
pp. 1-32
Author(s):  
MACIEJ DUNAJSKI ◽  
PAUL TOD
Keyword(s):  
Magnetic Field ◽  
Geodesic Flow ◽  
Isometry Group ◽  
Three Dimensional ◽  
First Integrals ◽  
Complete Integrability ◽  
Conformal Killing ◽  
Gravitational Instantons ◽  
Geodesic Equations ◽  
Jacobi Equations

Abstract We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the SO(3)–invariant gravitational instantons. On a hyper–Kähler four–manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self–dual magnetic field. In the case of the anti–self–dual Taub NUT instanton we integrate these equations completely by separating the Hamilton–Jacobi equations, and finding a commuting set of first integrals. This gives the first example of an integrable conformal geodesic flow on a four–manifold which is not a symmetric space. In the case of the Eguchi–Hanson we find all conformal geodesics which lie on the three–dimensional orbits of the isometry group. In the non–hyper–Kähler case of the Fubini–Study metric on $\mathbb{CP}^2$ we use the first integrals arising from the conformal Killing–Yano tensors to recover the known complete integrability of conformal geodesics.

scholarly journals Conformal killing tensors and covariant Hamiltonian dynamics

2014 ◽  
Vol 55 (12) ◽  
pp. 122702 ◽  
Author(s):  
M. Cariglia ◽  
G. W. Gibbons ◽  
J.-W. van Holten ◽  
P. A. Horvathy ◽  
P.-M. Zhang
Keyword(s):  
Hamiltonian Dynamics ◽  
Conformal Killing ◽  
Killing Tensors
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