Another important consequence of the wave-map structure is the fact that isometries of hyperbolic space map solutions to solutions.
Finally, it is convenient to introduce the kinetic energy density,
Note that this quantity is obtained by computing the time derivative of the wave map and then taking the squared length of the resulting vector field using the target metric. As a consequence, the kinetic energy is a geometric object. In other words, two solutions related by an isometry have the same kinetic energy density.
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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