| 31. | The conformal isometries of a domain therefore consist of holomorphic self-maps.
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| 32. | This action is an isometry of the word metric.
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| 33. | Allometric scaling is any change that deviates from isometry.
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| 34. | Thus at most three reflections suffice to reproduce any plane isometry . "
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| 35. | The identity is an isometry; nothing changes, so distance cannot change.
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| 36. | Together these are all the direct isometries in 3D.
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| 37. | Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry.
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| 38. | Suppose for the moment that " U " is an isometry.
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| 39. | That should narrow down the search for what isometries work to something finite.
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| 40. | The isometries form a proper subgroup of, namely PSU ( 2 ).
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