A note on the geometry of defromable bodies

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The geometric setting for many-body systems is extended to that for deformable bodies.
If the deformations of the body are restricted to general linear transformations,
one can set up a geometric theory of on the group $GL(n,{\bf R})$.
A suitable connection and a metric are defined on $GL(n,{\bf R})$.
Vibrational motions of the deformable body can be discussed accordingly.

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