2 WILHELM KLINGENBERG Clearly, when considering motions we can restrict ourselves to those of unit speed. That is, we can restrict the geodesic flow to the unit tangent space TXM of M. From the two aspects of a closed geodesic—a closed curve which is a geodesic and a geodesic (flow line) which is periodic—we elaborate the first one. We will consider a space formed by all closed curves in which the closed geodesics are characterized as the critical points of a functional. This idea goes back to Morse. In our exposition we will give a refined version of Morse's approach which has several advantages over the old one—in particular, it possesses a canonical 0(2)- action.
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